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# Convertible bond

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In finance, a convertible bond or convertible note or convertible debt (or a convertible debenture if it has a maturity of greater than 10 years) is a type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or cash of equal value. It is a hybrid security with debt- and equity-like features. [1] It originated in the mid-19th century, and was used by early speculators such as Jacob Little and Daniel Drew to counter market cornering. [2]

Finance is a field that is concerned with the allocation (investment) of assets and liabilities over space and time, often under conditions of risk or uncertainty. Finance can also be defined as the art of money management. Participants in the market aim to price assets based on their risk level, fundamental value, and their expected rate of return. Finance can be split into three sub-categories: public finance, corporate finance and personal finance.

In finance, a bond is an instrument of indebtedness of the bond issuer to the holders. The most common types of bonds include municipal bonds and corporate bonds.

Common stock is a form of corporate equity ownership, a type of security. The terms voting share and ordinary share are also used frequently in other parts of the world; "common stock" being primarily used in the United States. They are known as Equity shares or Ordinary shares in the UK and other Commonwealth realms. This type of share gives the stockholder the right to share in the profits of the company, and to vote on matters of corporate policy and the composition of the members of the board of directors.

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Convertible bonds are most often issued by companies with a low credit rating and high growth potential. Convertible bonds are also considered debt security because the companies agree to give fixed or floating interest rate as they do in common bonds for the funds of investor. To compensate for having additional value through the option to convert the bond to stock, a convertible bond typically has a coupon rate lower than that of similar, non-convertible debt. The investor receives the potential upside of conversion into equity while protecting downside with cash flow from the coupon payments and the return of principal upon maturity. These properties lead naturally to the idea of convertible arbitrage, where a long position in the convertible bond is balanced by a short position in the underlying equity.

A coupon payment on a bond is the annual interest payment that the bondholder receives from the bond's issue date until it matures.

Convertible arbitrage is a market-neutral investment strategy often employed by hedge funds. It involves the simultaneous purchase of convertible securities and the short sale of the same issuer's common stock.

From the issuer's perspective, the key benefit of raising money by selling convertible bonds is a reduced cash interest payment. The advantage for companies of issuing convertible bonds is that, if the bonds are converted to stocks, companies' debt vanishes. However, in exchange for the benefit of reduced interest payments, the value of shareholder's equity is reduced due to the stock dilution expected when bondholders convert their bonds into new shares.

Interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate. It is distinct from a fee which the borrower may pay the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.

Stock dilution, also known as equity dilution, is the decrease in existing shareholders’ ownership of a company as a result of the company issuing new equity. New equity increases the total shares outstanding which has a dilutive effect on the ownership percentage of existing shareholders. This increase in the number of shares outstanding can result from a primary market offering, employees exercising stock options, or by issuance or conversion of convertible bonds, preferred shares or warrants into stock. This dilution can shift fundamental positions of the stock such as ownership percentage, voting control, earnings per share, and the value of individual shares.

Convertible notes are also a frequent vehicle for seed investing in startup companies, as a form of debt that converts to equity in a future investing round.[ citation needed ] It is a hybrid investment vehicle, which carries the (limited) protection of debt at the start, but shares in the upside as equity if the startup is successful, while avoiding the necessity of valuing the company at too early a stage.

Seed money, sometimes known as seed funding or seed capital, is a form of securities offering in which an investor invests capital in a startup company in exchange for an equity stake in the company. The term seed suggests that this is a very early investment, meant to support the business until it can generate cash of its own, or until it is ready for further investments. Seed money options include friends and family funding, angel funding, and crowdfunding.

A startup or start up is a company initiated by individual founders or entrepreneurs to search for a repeatable and scalable business model. More specifically, a startup is a newly emerged business venture that aims to develop a viable business model to meet a marketplace need or problem. Founders design startups to effectively develop and validate a scalable business model. Hence, the concepts of startups and entrepreneurship are similar. However, entrepreneurship refers all new businesses, including self-employment and businesses that never intend to grow big or become registered, while startups refer to new businesses that intend to grow beyond the solo founder, have employees, and intend to grow large. Start ups face high uncertainty and do have high rates of failure, but the minority that go on to be successful companies have the potential to become large and influential. Some startups become unicorns, i.e. privately held startup companies valued at over $1 billion. ## Types Underwriters have been quite innovative and provided several variations of the initial convertible structure. Although no formal classification exists in the financial market it is possible to segment the convertible universe into the following sub-types: ### Vanilla convertible bonds • Vanilla convertible bonds are the most plain convertible structures. They grant the holder the right to convert into a certain number of shares determined according to a conversion price determined in advance. They may offer coupon regular payments during the life of the security and have a fixed maturity date where the nominal value of the bond is redeemable by the holder. This type is the most common convertible type and is typically providing the asymmetric returns profile and positive convexity often wrongly associated to the entire asset class: at maturity the holder would indeed either convert into shares or request the redemption at par depending on whether or not the stock price is above the conversion price. ### Mandatory convertibles • Mandatory convertibles are a common variation of the vanilla subtype, especially on the US market. Mandatory convertible would force the holder to convert into shares at maturity—hence the term "Mandatory". Those securities would very often bear two conversion prices, making their profiles similar to a "risk reversal" option strategy. The first conversion price would limit the price where the investor would receive the equivalent of its par value back in shares, the second would delimit where the investor will earn more than par. Note that if the stock price is below the first conversion price the investor would suffer a capital loss compared to its original investment (excluding the potential coupon payments). Mandatory convertibles can be compared to forward selling of equity at a premium. In finance, risk reversal can refer to a measure of the volatility skew or to an investment strategy. ### Reverse convertibles • Reverse convertibles are a less common variation, mostly issued synthetically. They would be opposite of the vanilla structure: the conversion price would act as a knock-in short put option: as the stock price drops below the conversion price the investor would start to be exposed the underlying stock performance and no longer able to redeem at par its bond. This negative convexity would be compensated by a usually high regular coupon payment. ### Packaged convertibles • Packaged convertibles or sometimes "bond + option" structures are simply a straight bonds and a call option/warrant wrapped together. Usually the investor would be able to then trade both legs separately. Although the initial payoff is similar to a plain vanilla one, the Packaged Convertibles would then have different dynamics and risks associated with them since at maturity the holder would not receive some cash or shares but some cash and potentially some share. They would for instance miss the modified duration mitigation effect usual with plain vanilla convertibles structures. ## Additional features Any convertible bond structure, on top of its type, would bear a certain range of additional features as defined in its issuance prospectus: • Conversion price: The nominal price per share at which conversion takes place, this number is fixed at the issuance but could be adjusted under some circumstance described in the issuance prospectus (e.g. Underlying stock split). You could have more than one conversion price for non-vanilla convertible issuances. • Issuance premium: Difference between the conversion price and the stock price at the issuance. • Conversion ratio: The number of shares each convertible bond converts into. It may be expressed per bond or on a per centum (per 100) basis. • Maturity/redemption date: Final payment date of a loan or other financial instrument, at which point the principal (and all remaining interest) is due to be paid. In some cases, for non-vanilla convertible bonds, there is no maturity date (i.e. perpetual), this is often the case with preferred convertibles (e.g. US0605056821). • Final conversion date: Final date at which the holder can request the conversion into shares. Might be different from the redemption date. • Coupon: Periodic interest payment paid to the convertible bond holder from the issuer. Could be fixed or variable or equal to zero. • Yield: Yield of the convertible bond at the issuance date, could be different from the coupon value if the bond is offering a premium redemption. In those cases the yield value would determine the premium redemption value and intermediary put redemption value. Convertibles could bear other more technical features depending on the issuer needs: • Call features: The ability of the issuer (on some bonds) to call a bond early for redemption. This should not be mistaken for a call option. A Softcall would refer to a call feature where the issuer can only call under certain circumstances, typically based on the underlying stock price performance (e.g. current stock price is above 130% of the conversion price for 20 days out of 30 days). A Hardcall feature would not need any specific conditions beyond a date: that case the issuer would be able to recall a portion or the totally of the issuance at the Call price (typically par) after a specific date. • Put features: The ability of the holder of the bond (the lender) to force the issuer (the borrower) to repay the loan at a date earlier than the maturity. These often occur as windows of opportunity, every three or five years and allow the holders to exercise their right to an early repayment. • Contingent conversion (aka CoCo): Restrict the ability of the convertible bondholders to convert into equities. Typically, restrictions would be based on the underlying stock price and/or time (e.g. convertible every quarter if stock price is above 115% of the conversion price). [3] Reverse convertibles in that respect could be seen as a variation of a Mandatory bearing a contingent conversion feature based. More recently some CoCo's issuances have been based on Tier-1 capital ratio for some large bank issuers. • Reset: Conversion price would be reset to a new value depending on the underlying stock performance. Typically, would be in cases of underperformance (e.g. if stock price after a year is below 50% of the conversion price the new conversion price would be the current stock price). • Change of control event (aka Ratchet): Conversion price would be readjusted in case of a take-over on the underlying company. There are many subtype of ratchet formula (e.g. Make-whole base, time dependent...), their impact for the bondholder could be small (e.g. ClubMed, 2013) to significant (e.g. Aegis, 2012). Often, this clause would grant as well the ability for the convertible bondholders to "put" i.e. ask for the early repayment of their bonds. • Non-dilutive: The non-dilutive feature has been popularised with the lower interest rates (e.g. in Euro) in order to make convertible issuance still attractive for issuers already benefitting from low interest charges in the straight bond market. In a non-dilutive placement, the issuer would simultaneously enter in an OTC option agreement with the underwriter (or a third party). This option would often match the strike of the convertible as well as its maturity. This would result in cancelling out the dilution in case of a conversion of the convertible at maturity if the stock price is above the strike. Typically, in order to fully prevent dilution the convertible prospectus would constraint possibility of early conversion. ## Structure and terminology Due to their relative complexity, convertible bond investors could refer to the following terms while describing convertible bonds: • Parity: Immediate value of the convertible if converted, typically obtained as current stock price multiplied by the conversion ratio expressed for a base of 100. May also be known as Exchange Property. • Bond floor: Value of the fixed income element of a convertible i.e. not considering the ability to convert into equities. • Premium: Defined as current convertible price minus the parity • Exchangeable bond: Convertible bond where the issuing company and the underlying stock company are different companies (e.g. XS0882243453, GBL into GDF Suez). This distinction is usually made in terms of risk i.e. equity and credit risk being correlated: in some cases the entities would be legally distinct, but not considered as exchangeable as the ultimate guarantor being the same as the underlying stock company (e.g. typical in the case of the Sukuk, Islamic convertible bonds, needing a specific legal setup to be compliant with the Islamic law). • Synthetic: synthetically structured convertible bond issued by an investment bank to replicate a convertible payoff on a specific underlying bond. Most reverse convertibles are synthetics. Please note the Packaged Convertibles (e.g. Siemens 17 DE000A1G0WA1) are not considered to be synthetics since the issuer would not be an Investment Bank: they would only act as underwriter. Similarly, a replicated structure using straight bonds and options would be considered as a package structure. ## Markets and Investor profiles The global convertible bond market is relatively small, with about 400 bn USD (as of Jan 2013, excluding synthetics), as a comparison the straight corporate bond market would be about 14,000 bn USD. Among those 400 bn, about 320 bn USD are "Vanilla" convertible bonds, the largest sub-segment of the asset class. Convertibles are not spread equally and some slight differences exist between the different regional markets: • North America: About 50% of the global convertible market, mostly from the USA (even if Canada is well represented in the Material sector). This market is more standardised than the others with convertible structures being relatively uniform (e.g. Standard Make-Whole take over features, Contingent Conversion @ 130%). Regarding the trading, the American convertible market is "centralised" around TRACE which helps in terms of price transparency. One other particularity of this market is the importance of the Mandatory Convertibles and Preferred especially for Financials (about 10-20% of the issuances in the US regional benchmarks). Most of the trading operation are based in New-York. • EMEA: European, Middle Eastern and African issuances are trading usually out of Europe, London being the biggest node followed by Paris and to a lesser extent Frankfurt and Geneva. It represents about 25% of the global market and shows a greater diversity in terms of structures (e.g. from CoCoCo's to French OCEANE). Because of that lack of standardisation, it is often considered to be more technical and unforgiving than the American market from a trading perspective. A very tiny amount of the volumes is traded on exchange while the vast majority is done OTC without a price reporting system (e.g. like TRACE). Liquidity is significantly lower than on the Northern American market. Trading convention are NOT uniform: French Convertibles would trade dirty in units while the others countries would trade clean in notional equivalent. • Asia (ex Japan): This region represents about 17% of the total market, with an overall structure similar to the EMEA market albeit with more standardisation across the issuances. Most of the trading is done in Hong-Kong with a minor portion in Singapore. • Japan: This region represents about 8% of the total market as of January 2013 in spite of being in the past comparable in size to the Northern American market. It mostly shrunk because of the low interest environment making the competitive advantage of lowering coupon payment less appealing to issuers. One key specificity of the Japanese market is the offering price of issuance being generally above 100, meaning the investor would effectively bear a negative yield to benefit from the potential equity underlying upside. Most of the trading is done out of Tokyo (and Hong-Kong for some international firms). Convertible bond investors get split into two broad categories: Hedged and Long-only investors. • Hedged/Arbitrage/Swap investors: Proprietary trading desk or hedged-funds using as core strategy Convertible Arbitrage which consists in, for its most basic iteration, as being long the convertible bonds while being short the underlying stock. Buying the convertible while selling the stock is often referred to as being "on swap". Hedged investors would modulate their different risks (e.g. Equity, Credit, Interest-Rate, Volatility, Currency) by putting in place one or more hedge (e.g. Short Stock, CDS, Asset Swap, Option, Future). Inherently, market-makers are hedged investors as they would have a trading book during the day and/or overnight held in a hedged fashion to provide the necessary liquidity to pursue their market making operations. • Long-only/Outright Investors: Convertible investors who will own the bond for their asymmetric payoff profiles. They would typically be exposed to the various risk. Please note that Global convertible funds would typically hedged their currency risk as well as interest rate risk in some occasions, however Volatility, Equity & Credit hedging would typically be excluded from the scope of their strategy. The splits between those investors differ across the regions: In 2013, the American region was dominated by Hedged Investors (about 60%) while EMEA was dominated by Long-Only investors (about 70%). Globally the split is about balanced between the two categories. ## Valuation See also: Bond option#Embedded options; Lattice model (finance)#Hybrid Securities. In theory, the market price of a convertible debenture should never drop below its intrinsic value. The intrinsic value is simply the number of shares being converted at par value times the current market price of common shares. The 3 main stages of convertible bond behaviour are: • In-the-money: Conversion Price is < Equity Price. • At-the-money: Conversion Price is = Equity Price. • Out-the-money: Conversion Price is > Equity Price. In-the-money CB's are considered as being within Area of Equity (the right hand side of the diagram). At-the-money CB's are considered as being within Area of Equity & Debt (the middle part of the diagram). Out-the-money CB's are considered as being within Area of Debt (the left hand side of the diagram) From a valuation perspective, a convertible bond consists of two assets: a bond and a warrant. Valuing a convertible requires an assumption of 1. the underlying stock volatility to value the option and 2. the credit spread for the fixed income portion that takes into account the firm's credit profile and the ranking of the convertible within the capital structure. Using the market price of the convertible, one can determine the implied volatility (using the assumed spread) or implied spread (using the assumed volatility). This volatility/credit dichotomy is the standard practice for valuing convertibles. What makes convertibles so interesting is that, except in the case of exchangeables (see above), one cannot entirely separate the volatility from the credit. Higher volatility (a good thing) tends to accompany weaker credit (bad). In the case of exchangeables, the credit quality of the issuer may be decoupled from the volatility of the underlying shares. The true artists of convertibles and exchangeables are the people who know how to play this balancing act. A simple method for calculating the value of a convertible involves calculating the present value of future interest and principal payments at the cost of debt and adds the present value of the warrant. However, this method ignores certain market realities including stochastic interest rates and credit spreads, and does not take into account popular convertible features such as issuer calls, investor puts, and conversion rate resets. The most popular models for valuing convertibles with these features are finite difference models as well as the more common binomial- and trinomial trees. Since 1991-92, most market-makers in Europe have employed binomial models to evaluate convertibles. Models were available from INSEAD, Trend Data of Canada, Bloomberg LP and from home-developed models, amongst others. These models needed an input of credit spread, volatility for pricing (historic volatility often used), and the risk-free rate of return. The binomial calculation assumes there is a bell-shaped probability distribution to future share prices, and the higher the volatility, the flatter is the bell-shape. Where there are issuer calls and investor puts, these will affect the expected residual period of optionality, at different share price levels. The binomial value is a weighted expected value, (1) taking readings from all the different nodes of a lattice expanding out from current prices and (2) taking account of varying periods of expected residual optionality at different share price levels. See Lattice model (finance)#Hybrid Securities. The three biggest areas of subjectivity are (1) the rate of volatility used, for volatility is not constant, and (2) whether or not to incorporate into the model a cost of stock borrow, for hedge funds and market-makers. The third important factor is (3) the dividend status of the equity delivered, if the bond is called, as the issuer may time the calling of the bond to minimise the dividend cost to the issuer. ## Uses for investors • Convertible bonds are usually issued offering a higher yield than obtainable on the shares into which the bonds convert. • Convertible bonds are safer than preferred or common shares for the investor. They provide asset protection, because the value of the convertible bond will only fall to the value of the bond floor: however in reality if stock price falls too much the credit spread will increase and the price of the bond will go below the bond floor. At the same time, convertible bonds can provide the possibility of high equity-like returns. • Also, convertible bonds are usually less volatile than regular shares. Indeed, a convertible bond behaves like a call option. Therefore, if C is the call price and S the regular share then ${\displaystyle \Delta ={\frac {\delta C}{\delta S}}\Rightarrow \delta C=\Delta \times \delta S.}$ In consequence, since ${\displaystyle 0<\Delta <1}$ we get ${\displaystyle \delta C<\delta S}$, which implies that the variation of C is less than the variation of S, which can be interpreted as less volatility. • The simultaneous purchase of convertible bonds and the short sale of the same issuer's common stock is a hedge fund strategy known as convertible arbitrage. The motivation for such a strategy is that the equity option embedded in a convertible bond is a source of cheap volatility, which can be exploited by convertible arbitrageurs. • In limited circumstances, certain convertible bonds can be sold short, thus depressing the market value for a stock, and allowing the debt-holder to claim more stock with which to sell short. This is known as death spiral financing. ## Uses for issuers ### Lower fixed-rate borrowing costs • Lower fixed-rate borrowing costs. Convertible bonds allow issuers to issue debt at a lower cost. Typically, a convertible bond at issue yields 1% to 3% less than straight bonds. ### Locking into low fixed–rate long-term borrowing • Locking into low fixed–rate long-term borrowing. For a finance director watching the trend in interest rates, there is an attraction in trying to catch the lowest point in the cycle to fund with fixed rate debt, or swap variable rate bank borrowings for fixed rate convertible borrowing. Even if the fixed market turns, it may still be possible for a company to borrow via a convertible carrying a lower coupon than ever would have been possible with straight debt funding. ### Higher conversion price than a rights issue strike price • Higher conversion price than a rights issue strike price. Similarly, the conversion price a company fixes on a convertible can be higher than the level that the share price ever reached recently. Compare the equity dilution on a convertible issued on, say, a 20 or 30pct premium to the higher equity dilution on a rights issue, when the new shares are offered on, say, a 15 to 20pct discount to the prevailing share price. ### Voting dilution deferred • Voting dilution deferred. With a convertible bond, dilution of the voting rights of existing shareholders only happens on eventual conversion of the bond. However convertible preference shares typically carry voting rights when preference dividends are in arrears. Of course, the bigger voting impact occurs if the issuer decides to issue an exchangeable rather than a convertible. ### Increasing the total level of debt gearing • Increasing the total level of debt gearing. Convertibles can be used to increase the total amount of debt a company has in issue. The market tends to expect that a company will not increase straight debt beyond certain limits, without it negatively impacting upon the credit rating and the cost of debt. Convertibles can provide additional funding when the straight debt “window” may not be open. Subordination of convertible debt is often regarded as an acceptable risk by investors if the conversion rights are attractive by way of compensation. ### Maximising funding permitted under pre-emption rules • Maximising funding permitted under pre-emption rules. For countries, such as the UK, where companies are subject to limits on the number of shares that can be offered to non-shareholders non-pre-emptively, convertibles can raise more money than via equity issues. Under the UK’s 1989 Guidelines issued by the Investor Protection Committees (IPCs) of the Association of British Insurers (ABI) and the National Association of Pension Fund Managers (NAPF), the IPCs will advise their members not to object to non pre-emptive issues which add no more than 5pct to historic non-diluted balance sheet equity in the period from AGM to AGM, and no more than 7.5pct in total over a period of 3 financial years. The pre-emption limits are calculated on the assumption of 100pct probability of conversion, using the figure of undiluted historic balance sheet share capital (where there is assumed a 0pct probability of conversion). There is no attempt to assign probabilities of conversion in both circumstances, which would result in bigger convertible issues being permitted. The reason for this inconsistency may lie in the fact that the Pre Emption Guidelines were drawn up in 1989, and binomial evaluations were not commonplace amongst professional investors until 1991-92. ### Premium redemption convertibles • Premium redemption convertibles such as the majority of French convertibles and zero-coupon Liquid Yield Option Notes (LYONs), provide a fixed interest return at issue which is significantly (or completely) accounted for by the appreciation to the redemption price. If, however, the bonds are converted by investors before the maturity date, the issuer will have benefited by having issued the bonds on a low or even zero-coupon. The higher the premium redemption price, (1) the more the shares have to travel for conversion to take place before the maturity date, and (2) the lower the conversion premium has to be at issue to ensure that the conversion rights are credible. ### Takeover paper • Takeover paper. Convertibles have a place as the currency used in takeovers. The bidder can offer a higher income on a convertible than the dividend yield on a bid victim’s shares, without having to raise the dividend yield on all the bidder’s shares. This eases the process for a bidder with low-yield shares acquiring a company with higher-yielding shares. Perversely, the lower the yield on the bidder’s shares, the easier it is for the bidder to create a higher conversion premium on the convertible, with consequent benefits for the mathematics of the takeover. In the 1980s, UK domestic convertibles accounted for about 80pct of the European convertibles market, and over 80pct of these were issued either as takeover currency or as funding for takeovers. They had several cosmetic attractions. The pro-forma fully diluted earnings per share shows none of the extra cost of servicing the convertible up to the conversion day irrespective of whether the coupon was 10pct or 15pct. The fully diluted earnings per share is also calculated on a smaller number of shares than if equity was used as the takeover currency. In some countries (such as Finland) convertibles of various structures may be treated as equity by the local accounting profession. In such circumstances, the accounting treatment may result in less pro-forma debt than if straight debt was used as takeover currency or to fund an acquisition. The perception was that gearing was less with a convertible than if straight debt was used instead. In the UK the predecessor to the International Accounting Standards Board (IASB) put a stop to treating convertible preference shares as equity. Instead it has to be classified both as (1) preference capital and as (2) convertible as well. Nevertheless, none of the (possibly substantial) preference dividend cost incurred when servicing a convertible preference share is visible in the pro-forma consolidated pretax profits statement. The cosmetic benefits in (1) reported pro-forma diluted earnings per share, (2) debt gearing (for a while) and (3) pro-forma consolidated pre-tax profits (for convertible preference shares) led to UK convertible preference shares being the largest European class of convertibles in the early 1980s, until the tighter terms achievable on Euroconvertible bonds resulted in Euroconvertible new issues eclipsing domestic convertibles (including convertible preference shares) from the mid 1980s. ### Tax advantages • Tax advantages. The market for convertibles is primarily pitched towards the non taxpaying investor. The price will substantially reflect (1) the value of the underlying shares, (2) the discounted gross income advantage of the convertible over the underlying shares, plus (3) some figure for the embedded optionality of the bond. The tax advantage is greatest with mandatory convertibles. Effectively a high tax-paying shareholder can benefit from the company securitising gross future income on the convertible, income which it can offset against taxable profits. ## 2010 U.S. Equity-Linked Underwriting League Table RankUnderwriterMarket Share (%)Amount ($m)
1J.P. Morgan21.0$7,359.72 2Bank of America Merrill Lynch15.3$5,369.23
3Goldman Sachs & Co12.5$4,370.56 4Morgan Stanley8.8$3,077.95
5Deutsche Bank AG7.8$2,748.52 6Citi7.5$2,614.43
7Credit Suisse6.9$2,405.97 8Barclays Capital5.6$1,969.22
9UBS4.5$1,589.20 10Jefferies Group Inc4.3$1,522.50

Source: Bloomberg

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The following outline is provided as an overview of and topical guide to finance:

A reverse convertible security or convertible security is a short-term note linked to an underlying stock. The security offers a steady stream of income due to the payment of a high coupon rate. In addition, at maturity the owner will receive either 100% of the par value or, if the stock value falls, a predetermined number of shares of the underlying stock. In the context of structured product, a reverse convertible can be linked to an equity index or a basket of indices. In such case, the capital repayment at maturity is cash settled, either 100% of principal, or less if the underlying index falls conditional on barrier is hit in the case of barrier reverse convertibles.

An inverse floating rate note, or simply an inverse floater, is a type of bond or other type of debt instrument used in finance whose coupon rate has an inverse relationship to short-term interest rates. With an inverse floater, as interest rates rise the coupon rate falls. The basic structure is the same as an ordinary floating rate note except for the direction in which the coupon rate is adjusted. These two structures are often used in concert.

Foreign currency convertible bonds (FCCBs) are a special category of bonds. FCCBs are issued in currencies different from the issuing company's domestic currency. Corporates issue FCCBs to raise money in foreign currencies. These bonds retain all features of a convertible bond, making them very attractive to both the investors and the issuers.

## References

1. Scatizzi, Cara (February 2009). "Convertible Bonds". The AAII Journal. Retrieved 8 September 2015.
2. Jerry W. Markham (2002). A Financial History of the United States: From Christopher Columbus to the Robber Barons. M. E. Sharpe. p. 161. ISBN   0-7656-0730-1.
3. Hirst, Gary (June 21, 2013). "Cocos: Contingent Convertible Capital Notes and Insurance Reserves". garyhirst.com. Retrieved April 13, 2014.


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Math Comparisons

On the Pre-Assessment I did really well because I only got 2 incorrect. On the other hand, my summative was okay. I got a few incorrect but that is normal for me.

There are many comparisons I can make and I have one right now. For instance, for the pre-assessment, in the problem where I had to write it greatest to least, I did it correct. But for the summative I didn’t do it right. An evidence is, I wrote from least to great instead of the opposite consecutive order.

Next, I also improved my recognition towards expanded form and like all those forms. For example, when we were suppose to write the number in expanded form in our pre-assessment, I accidentally wrote it in word form. But for the summative, I looked at the directions more carefully so I do it correct.

Finally, my order of operations improved. Even in both of them I did not get wrong, I still think I improved. To add on, I am saying I can see I do it a lot quicker in the summative but still show my work in an efficient way. I can get the numbers out of my head easily and smoothly because I had a lot of practice. For the pre-assessment, I did know how to do it but I just felt like I could improve just a bit and I did in the summative.

Looking at both of the tests I can point out the differences between them. I really did try to improve on the summative and I somewhat was able to. Even I only got beginning to meet I still see big improvements I made after the unit.

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## Is second order logic really first order?

November 6, 2008

Nowadays, I guess, a lot more people are sympathetic to the idea that second order logic is real logic than in Quine’s day due to the popularity of plural logic. However, this falls short of full second order logic by quite a long way due to the fact that it can’t quantify over relations. For example, you can’t state various facts about sizes or the axiom of choice.

In the first order case, the question seems to be more tractable. If we identify the logical vocabulary as those terms that are not sensitive to the particular identities of the individuals (i.e. whose extensions remain unchanged if you permute the domain) then we get the cardinality quantifiers and arbitrary unions of the cardinality quantifiers as logical terms. McGee confirms the intuition that these truly are logical by showing that the permutation invariant (first order) vocabulary are precisely those defineable from intuitively logical operations: negation, identity, arbitrary conjunctions, universal quantification with respect to an arbitrary block of variables. Admittedly, this language ($L_{\infty, \infty}$) is not a language that anyone can speak, but that is a deficiency on our part, and should not place constraints on logic. Thus, first order quantification seems to be ontologically innocent, even for quantifiers like ‘there are uncountably many F’s’.

Indeed, similar results hold if we allow second order quantifiers. They are also permutation invariant, and conversely, the permutation invariant second order quantifiers is precisely those that can be defined in the equivalent of $L_{\infty, \infty}$ with arbitrary blocks of second order quantifiers too. But the difference here, it seems, is that it is not clear that second order quantification over relations is ontologically innocent. Sure, plural quantifiers are, but as soon as we leave the realm of monadic quantification there is less reason to think so (although some have suggested that you can get around it: e.g. Burgess, and Rayo and Linnebo.)

Anyway, I was wondering if it would be possible to reduce second order quantification to first order quantification in our infinitary language. If this were possible then we could happily use the second order quantifiers and safely know that the are not ontologically committing, because they are definable using first order vocabulary.

I think you can do it, but I’m not entirely sure so this might be wrong. Let $\kappa$ be antizero – the size of everything. For each second order variable X of the language keep aside $\kappa$ many variables: $x_\alpha$ for $\alpha \leq \kappa$. Then define a translation schema as follows: [UPDATE: I reformulated it slightly so that it wasn’t quite so confusing.] For a subset of the domain, I, we define the translate of $\phi$ with repsect to I as follows:

$(Xx)^I \mapsto \bigvee_{\alpha \in I}x=x_\alpha$

$(\forall X \phi)^I \mapsto \forall x_1 \ldots x_\kappa(\forall y\bigvee_{\alpha \leq \kappa}x_\alpha=y \rightarrow \bigvee_{J \subseteq \kappa} (\phi)^J)$

For the other connectives and quantifiers translation just commutes in the natural way. A couple of notes: this isn’t like $L_{\infty, \infty}$ in that it must allow truly arbitrary disjunctions and quantifications (including proper class length conjunctions.) Secondly, it’s not really as simple a translation as it looks because in the first clause I left I “free”, to be later “bound” by an earlier application of the second translation clause. What this really means is that the length of the disjunction in the first clause is really determined by when it is called in the second clause. Lastly – that’s just monadic quantification, which we already had – but it seems it will extend nicely to polyadic second order quantifiers (this time we disjoin $(x = x_\alpha \wedge y = y_\alpha)$ instead.)


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# Need Help Understanding an Equality

I'm mostly trying to understand how the expression in brackets becomes a partial derivative.

I know I end up with 0/0 if I replace all deltaz with 0, so that leads me to belive L'hopitals rule is used here. I just don't see how I could take L hopitals when I have two variables..

#### Attachments

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Related Calculus and Beyond Homework Help News on Phys.org
Simon Bridge
Homework Helper
Take the limit as Δz→0 and the LHS becomes the definition for the partial derivative.

Last edited:
? But wouldn't that give me 0/0 if I take the limit directly?

Simon Bridge
Homework Helper
How? Where?

I have to go ... so, notice:
##\Delta z## only appears on the LHS, so the limit dos not affect the RHS at all.
It appears inside the function ##v(z,t)## in the numerator.
How is this different from a regular derivative with only one variable?

delta z is in the numerator and in the denominator on the LHS. I'm not sure what you're trying to say.

Simon Bridge
Homework Helper
Ahhh... I think I get where you are coming from.

The fact that delta-z appears inside a function in the numerator makes all the difference.
remember, the limit is what happens as delta-z gets very close to zero ... not what happens when delta-z actually is equal to zero. delta-z never reaches zero.

I'm guessing you've not used this sort of expression before:
$$\frac{d}{dx}f(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$$

You could imagine that in the limit, f(x+h)=f(x), which makes the expression evaluate to 0/0.
But that does not work for all possible f(x) - I only need one counter-example to show it's not always true, watch:

example: f(x)=x
$$\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}= \lim_{h\rightarrow 0}\left [ \frac{(x+h)-x}{h}\right]=\lim_{h\rightarrow 0}\left[ \frac{h}{h}\right]=\lim_{h\rightarrow 0}[1]=1$$ ... see? Since all the h's cancel out, the limit evaluates into something sensible.

The trick is to do the algebra with the aim of getting the h out of the denominator. Otherwise that could be a problem.

example f(x)=x^2 ... try it.

Now back to your example - put v(z,t)=z/t in the LHS, and take the limit delta-z approaches zero.

Last edited:
HallsofIvy
Homework Helper
Surely, if you are looking at problems like this, you have taken Calculus? The definition of the "derivative of f(x) at x= a" is
$$\lim_{h\to 0}\frac{f(a+ h)- f(a)}{h}$$

Obviously, if you simple "set h equal to 0" you will get the meaningless "0/0". That's the whole point of using the "limit". Taking the limit "as h goes to 0" is NOT the same as setting h= 0. You should have learned that in introductory Calculus.

Ahhh... I think I get where you are coming from.

The fact that delta-z appears inside a function in the numerator makes all the difference.
remember, the limit is what happens as delta-z gets very close to zero ... not what happens when delta-z actually is equal to zero. delta-z never reaches zero.

I'm guessing you've not used this sort of expression before:
$$\frac{d}{dx}f(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$$

You could imagine that in the limit, f(x+h)=f(x), which makes the expression evaluate to 0/0.
But that does not work for all possible f(x) - I only need one counter-example to show it's not always true, watch:

example: f(x)=x
$$\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}= \lim_{h\rightarrow 0}\left [ \frac{(x+h)-x}{h}\right]=\lim_{h\rightarrow 0}\left[ \frac{h}{h}\right]=\lim_{h\rightarrow 0}[1]=1$$ ... see? Since all the h's cancel out, the limit evaluates into something sensible.

The trick is to do the algebra with the aim of getting the h out of the denominator. Otherwise that could be a problem.

example f(x)=x^2 ... try it.

Now back to your example - put v(z,t)=z/t in the LHS, and take the limit delta-z approaches zero.
I end up with

{ [ (z/t) + Δz] - (z/t) } / Δz

then

Δz / Δz

then

1

then taking the limit I get

1

Or am I supposed to do

{[(z + Δz)/t] - (z/t)} / Δz

[(z/t) + (Δz/t) -(z/t)] / Δz

(Δz/t) / Δz

1/t

How does this get me to the partial derivative with respect to z and how would I know that doing all this wouldn't give me a partial with respect to t instead?

Also, was (z/t) arbitrary? Or would something like (zt) have worked?

Simon Bridge
Homework Helper
You use the normal rules for substitution:

If ##v(z,t)=z/t##, then ##v(z+Δz,t) = (z+Δz)/t##

i.e every time you see a z, you replace it with z+Δz

So you have the LHS limit = 1/t - compare that with the partial derivative.
(Do you know how to take a partial derivative?)

How does this get me to the partial derivative of with respect to z and how would I know that doing all this wouldn't give me a partial with respect to t instead?
The partial derivative of ##v(z,t)## with respect to ##t## would be:
$$\frac{\partial}{\partial t}v(z,t)=\lim_{\Delta t\rightarrow 0}\frac{v(z,t+\Delta t)-v(z,t)}{\Delta t}$$

In general,
If you have a function ##f(\vec{x})## of ##N## variables ##\vec{x}=(x_1,x_2,\cdots ,x_N)##
Then the partial derivative wrt the nth variable, where ##1\leq n \leq N##, is:
$$\frac{\partial}{\partial x_n}f(\vec{x})=\lim_{\Delta x_n\rightarrow 0}\frac{f(\cdots, x_n+\Delta x_n,\cdots)-f(\cdots,x_n,\cdots)}{\Delta x_n}$$
... note: if you don't understand that notation you have a serious problem!

Also, was (z/t) arbitrary? Or would something like (zt) have worked?
Do it and see :)

The definition works for any differentiable function. It would have worked for ##v(z,t)=z## or ##v(z,t)=t## ... whatever.

Do you know how to differentiate functions by rule instead of using the definition?
i.e. can you do: $$\frac{d}{dx}(ax^2+bx+e^{cx})$$


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# Need to know More About Happiness Health?

Sure, consuming nicely could be laborious — household schedules are hectic and seize-and-go comfort food is available. Thus, the last word term in Brandon’s definition should be expanded to $$f(E,\sigma^2,\ldots)$$, the place the ellipsis indicate the extra statistical parts which usually mix with or cancel the variance to search out out fitness levels. Health may be outlined as bodily, psychological, and social wellbeing, and as a useful resource for living a full life. To guard the health and security of Albertans, public health orders may be legally-enforced and fines issued for violations. Sustainable diets are protecting and respectful of biodiversity and ecosystems, culturally acceptable, accessible, economically honest and reasonably priced; nutritionally ample, safe and healthy; whereas optimising pure and human resources’.

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## By lifting heavy weight you tear your muscle fibers.

Many occasions in each day life we go to places like coffee shops and there are temptations galore …


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# AML supervision at central banks: 2022 survey

Kroll explores why many central banks are investing in skills and data to tackle money laundering, but resourcing constraints are preventing stronger action, as Central Banking’s survey data reveals.

### Key findings

• Anti-money laundering (AML) teams are typically fairly small. Central banks with a dedicated team report a median size of 18 staff members.
• The focus remains on traditional financial institutions – 81% say they oversee banks, but only 19% oversee crypto firms and 14% fintech firms more broadly.
• Few financial firms seem to lose their licences because of AML breaches. Only 24% of respondents have rescinded at least one licence in the past three years.
• Cross-border financial flows are seen as the number one source of risk, with 76% of respondents warning this is a key concern.
• More than half of respondents say a lack of resources is hampering their AML efforts.
• On- and off-site inspections remain key tools for supervisors looking to address money laundering risks.
• Two-thirds of respondents report using data analytics for AML purposes. Of these, 71% say they use forms of automated data collection.
• There are many hurdles to better use of data. The wide range in the size and complexity of supervised entities is a concern (67% of respondents), followed by a lack of technical tools (62%).
• Collaboration, including data sharing, is common on a domestic level. But authorities are much less likely to collaborate and proactively share data with global counterparts.

The two years since the outbreak of Covid‑19 have been a boon for many criminals. The rise of digital finance – particularly crypto assets – has given them new ways to finance crime, including terrorism, and new channels through which to launder money. Authorities have been distracted, their attention and resources devoted to fighting the pandemic and its economic fallout. Meanwhile, in many countries, generous government support schemes have created even more fertile ground for fraud.

### Risk factors

Comfortably the number one risk factor was international financial flows, reported as a key concern by 76% of respondents. Corruption came in at number two (57%), followed by large cash payments (48%) (see figure 2).

Echoing figure 1, the data shows that central banks still view newer threats, such as crypto assets and fintech, as lesser concerns. Only 5% reported crypto and fintech as major risk factors in their jurisdictions.

This may be starting to change. The Financial Stability Board’s latest report into crypto assets noted crypto markets were on a path to becoming systemically important. But they are not there yet.

### Supervision: tools and challenges

Despite the impact of Covid-19, the most commonly reported supervisory tool was on-site inspections of financial firms, in use at 86% of respondents. A further 81% reported off-site, desk-based reviews as a key tool. The latter has grown in importance since the advent of social distancing rules, but it remains to be seen whether the balance between on-site and off-site reviews has permanently shifted.

Central banks reported having conducted anything from just one supervisory inspection in the past year to as many as 463, with a median of 12 inspections (see figure 3).

Many central banks commented that they used risk-based approaches to supervising money laundering/terrorist financing risks, as advocated by the FATF. One advanced economy central bank in the Asia-Pacific region said it employed risk-based supervision. This central bank said it had moved away from “fixed on-site inspection cycles” towards “more dynamic and timely” interventions. The respondent highlighted three key tools: use of data analytics to identify high-risk activities; supervisory interventions to “dynamically disrupt” high-risk activities; and targeted inspections to direct remediation at high-risk firms.

A second central bank in Asia-Pacific stressed the importance of its AML risk rating system, which allows supervisors to make systematic assessments of firms’ risk profiles. This feeds into the wider process of risk-based supervision. To further support these efforts, the institution carries out periodic sectoral risk assessments.

Risk-based supervision could help central banks meet other objectives as well. A central bank in the Americas commented that it had implemented a simplified due diligence approach to allow banks to set up accounts for vulnerable people in society, “including low-income and undocumented persons”.

Many respondents said they employed regular reviews of AML risks across their whole jurisdiction. Central banks reported their most recent review fell in years ranging from 2013–22. The most common response was 2019.

Central banks face an array of challenges when it comes to improving their AML supervision. Over half (57%) said limited resources was a major obstacle. The second most important was data gaps, reported by 48% of respondents, followed by data quality, at 29% (see figure 4).

### Data: analytics and obstacles

Exactly two-thirds of respondents said they use data analytics to help them identify AML risks. Of these, the most commonly reported data tool was the use of automated data collection (in use at 71% of respondents that apply data analytics). The use of data in external public records was also common, at 64% of respondents. Much less used was AI or machine learning, in use at just one central bank. Big data or ‘alternative’ data was used by three (21%).

The figures show a significant minority of central banks in the sample (33%) do not use data analytics in their AML work, suggesting this could be an area of expansion in future years (see figure 5).

However, for data use to become more widespread and effective, central banks will have to overcome a range of obstacles. The most commonly reported problem was the sheer range of institutions on which data must be gathered, given their differing size and complexity – 67% of central banks said this was a problem. A further 62% said a lack of technical tools was holding them back, while 52% mentioned a lack of resources (see figure 6).

At the other end of the spectrum, AML definitions (19%), lengthy processes (24%) and data duplication or incompatibility (both 29%) were less commonly reported as challenges.

### Resourcing

The broad trend appears to be towards either greater resourcing of AML functions, particularly in the staff and training categories, or constant levels of resourcing. One central bank reported that its staffing resource had fallen in 2021, and one other reported that its training resources had fallen (see figure 7).

Somewhat less seems to be invested in data platforms, hardware – for instance for data processing – and cloud platforms. Only 14 central banks commented on cloud resourcing, which may indicate that use of the cloud is still relatively limited, at least for AML purposes.

Given that central banks report a lack of resources as a key concern, more investment in AML may be needed. One central bank in Africa commented that recent reforms to the AML function had led to greater co-operation with local and overseas authorities, which had the additional advantage of allowing pooling of resources.

### Collaboration and data sharing

The data suggests authorities have closer ties to domestic authorities than to their counterparts abroad, which could hamper efforts to improve information and data sharing. Since central banks report international financial flows are a key concern, strengthening global ties seems an important priority.

It is common to have a body tasked with co-ordinating AML/CFT authorities domestically. Only four central banks (19%) said they did not have such a body in their jurisdiction. Most of those that have a body mention that this is either the country’s financial intelligence unit or a council specifically formed to co-ordinate AML matters.

Similarly, most central banks report that they share data on suspicious activity domestically. Two-thirds say they share data on a proactive basis, and another 23% say they provide data on request. Only 10% say they do not share data at all domestically (see figure 8).

A central bank in the Americas reports it is undertaking a project to centralise know-your-customer data at a national level. Financial institutions and regulators will be able to access the data. The project is expected to enter production in July 2022.

All respondents say they are engaged with some form of international collaboration on AML. Regional groupings are the most common (76%), followed by bilateral co-operation (67%) and international bodies (48%).

However, many central banks (38%) do not share any data on suspicious transactions internationally. A further 43% said they share data on request, while only 19% of central banks share data proactively on an international level.

This feature forms part of the Central Banking focus report, Anti-money laundering and countering the financing of terrorism 2022

You need to sign in to use this feature. If you don’t have a Central Banking account, please register for a trial.


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# The solar resource

Solar energy is the source of all energy on earth, available to us in a number of derivatives. Plant matter for example, which relies on solar energy for nutrition, experiences natural compression and decomposition over millions of years to form the the fossil fuels we use today for electrical generation and transportation. Other examples of this can be seen in use of biomass for fuel or the harvesting of wind energy which is reliant on solar heated air for the formation of currents.

We are also able to utilize the solar resource directly. Solar thermal technologies take advantage of this resource to heat a working fluid that can transfer energy to an air stream or water for domestic or commercial use. Solar Photovoltaic or PV devices exploit various materials (principally Silicon) that experience sub-atomic variations when exposed to solar energy in order to induce an electric current. Both solar PV and thermal technologies provide a useful source of energy with little to no moving parts, no pollution and very little embodied energy.

In order to effectively design a solar energy system, an understanding of the available solar resource at the location of interest is required. This article aims to provide readers with an understanding of the earth's solar resource and introduces the tools required to perform a basic analysis. A brief overview of solar radiation measurement techniques and performance modeling will also be provided.

# The Sun

All of the energy available on Earth is derived from the sun. We can model the sun's surface as blackbody. At a specific temperature, approximately 5777K for the sun, a blackbody emits energy with a unique radiation spectrum (Table 1).

Ultraviolet Visible Infrared
Wavelength (${\mu}$m) 0 - 0.38 0.38 - 0.78 0.78 - Inf
Fraction in Range 0.064 0.480 0.456
Energy in Range (W/m2) 87 656 623

The spectrum is divided into three broad ranges classified as ultraviolet, visible and infrared which transmit radiation at varying intensities. The highest intensities are found within the visible spectrum, peaking at a wavelength close to 0.5um. Averaged over the entire surface, the power density of the sun is found to be approximately 63 x 10 W/m2.

The sun emits radiation in all directions, however only a portion of this energy is intercepted by the Earth. The intercepted radiation for any body in space is defined as follows:

Ho = (Rsun2 / D2) Hsun

Where Ho is the intercepted power density

Hsun is the power density of the sun

D is the distance between the sun and body of interest

For Earth, the distance to the sun is about 1.495 x 1011m. This provides an Earth intercepted value of around 1353 W/m2.
Figure 1: Earth Bound Radiation Losses[2]
This number is known as the Earth's solar constant and is often referred to as extra-terrestrial radiation.

Terrestrial radiation, that is radiation hitting the Earth's surface, varies widely with geographical location, local atmospheric conditions, time of day and time of year. Some regions are more suspect to variability in terrestrial radiation than others, depending on the amount of weather fluctuations experienced. For example, desert regions tend to demonstrate consistent weather patterns thereby providing relatively consistent values of terrestrial radiation.

As the radiation passes through the atmosphere the following mechanism determine the amount of radiation that will reach the Earth's surface:

Absorption – Certain molecules in the atmosphere posses high photon absorption properties. For example, water vapour (H2O) and CO2 absorb far infrared radiation and ozone (O3) absorbs ultraviolet radiation. Energy that is absorbed here is unavailable for use by solar panels.

Reflection – In addition to absorption, radiation can also be reflected off of particles in the atmosphere. Radiation that is reflected a number of times before eventually reaching the Earth's surface is known as diffuse radiation. A portion of the incoming radiation may also be lost completely by reflection back into space.

No Interaction – About 70% of the incoming radiation will pass through the atmosphere undisturbed. This is known as beam or direct radiation.

Figure 2: Beam and Diffuse Radiation

The losses due to atmospheric effects do not cause any major dips in the radiation spectrum. Rather, the impact is an overall reduction in the intensity of the entire spectrum. Depending on the time of the day, the sun's apparent position in the sky changes and as a result the length of atmosphere that the radiation must travel through also changes. When the sun is directly overhead, this length is referred to as the air mass (AM). Moving away from this overhead position, the travel distance required to hit the collecting surface increases. Figure 3 is simple schematic showing this effect.

A simple calculation can be performed to quickly determine the air mass:
Figure 3: Air Mass as Sun Moves Across the Sky

AM = 1 / cos ${\theta}$

In order to account for the curvature of the atmosphere the following formula can be applied:

AM = 1 / [cos ${\theta}$ + 0.50572 (96.07995 – ${\theta}$) - 1.6364] [3]

The air mass effect can also be visually understood by noting that the sun appears white (high intensity) when it is directly overhead and much redder (low intensity) during the morning and evening hours. If the air mass is known, then the resulting radiation intensity can be calculated as follows:

ID = 1.353 [(1 - 0.14h) 0.7(AM^0.678) + 0.14h][3]

IG = 1.1 ID

*where h is the height above sea level

The variability in the radiation received at the Earth's surface requires the identification of a standard to allow for fair testing and comparison of solar energy systems. This is has been defined as AM1.5 and is representative of the total radiation hitting the Earth's surface, which is found to be approximately 1000W/m2 (beam + diffuse). This value is often used to perform preliminary calculations for predicting how a system will perform. The AM1.5 spectrum is shown in Figure 4.

Figure 4: Global Radiation Spectrum AM1.5

Accounting for the losses discussed above, the amount of energy reaching the Earth's surface every hour is still greater than the amount of energy used by the world's population in an entire year. Herein lies the motivation to design and implement solar thermal and solar PV systems.

Additional Information Weather data will often include a measure known as the clearness indexW. This value is the ratio of received radiation on a horizontal plane to extra-terrestrial radiation based on ground and satellite measurements.

For theoretical calculations a number of sky models have been developed. The most basic model assumes that diffuse component of radiation is constant regardless of orientation. This means that all of the diffuse radiation is derived only from atmospheric scattering and equally from all directions. The Isotropic Sky model applies the same assumption but also includes diffuse radiation resulting from ground reflected radiation.

Two main phenomena, circumsolar radiation and horizon brightening, are ignored by the preceding models. Circumsolar radiation refers to the greater concentration of diffuse radiation existing in the sky immediately around the location of the sun relative to the remainder of the sky; Horizon brightening refers to the greater concentration of diffuse radiation existing on the horizon relative to the remainder of sky. These two components are accounted for in the Anistropic Sky model, however are generally not required for system performance analysis.

#  Describing the Sun's Location

In order to calculate the air mass, the sun's position in the sky needs to be defined. In addition, the apparent position of the sun in the sky will significantly impact the amount of radiation intercepted by our collecting surface. This section will define a number of key terms and outline how to calculate the radiation that is intercepted by a given collector; followed by an example in order to further clarify the methodology.

Table 2: Solar Radiation Key Terms[4]
Term Definition Diagram
Solar Noon Time when the sun is directly overhead position of interest. Each hour away from this position corresponds to a 15o deviation (hour angle).
Zenith Angle (θz) The angle between the vertical and the line to the sun. This is also the angle of incidence on a horizontal surface for beam radiation. Additionally, the Solar Altitude angle is defined as the compliment of the zenith angle.
Solar Azimuth Angle (γs) The deviation angle from due South for the projection of the sun's position on the horizontal plane (-180o for Each, +180o for West)
Surface Azimuth Angle (γ) The deviation angle from due South for the surface's normal vector projected onto the horizontal plane (-180o for Each, +180o for West)
Declination Angle (δ) The angular position of the sun (at solar noon) with respect to the plane of the equator. The angle varies seasonally due to the Earth's tilt and can be calculated for a given day using:

δ = 23.45 sin[ 360 (284 + n) / 365 ]
where n is day of the year

Slope (β) Angle between the collecting surface and the horizontal plane. In order to maximize the solar yield over the entire year, this angle should be set equal to the latitude. Steeper angles can be utilized to optimize for winter months. Likewise, shallow angles are used to optimize solar yield during the summer months.
Irradiance The rate at which radiant energy is incident on a surface per unit area of surface (W/m2) -
Irradiation The incident energy per unit area on a surface (integration of irradiance over a specific time J/m2

-

Insolation Irradiation applied specifically to solar energy -

## Calculating the Position of the Sun and Angle of Incidence

This section will outline the methodology and equations required to calculate the sun’s position and the angle of incidence for a known surface at a given time and location.

Initial Calculations and known values:

Angle of Declination (δ) = 23.45 sin[ 360 (284 + n) / 365 ]

Hour Angle (ω)= (Number of Hours from Solar Noon) x 15o

Surface Azimuth (γ) = Orientation of surface measured from due South

Slope (β): Slope of surface

Latitude(Φ) of Location

Using these variables the consine of the angle of incidence of beam radiation on the surface is:

cosθ = sinδ sinΦ cosβ – sinδ cosΦ sinβ cosγ + cosδ cosΦ cosβ cosω + cosδ sinΦ sinβ cosγ cosω + cosδ sinβ sinγ sinω[5]

*For surfaces facing directly south/north the equation is simplified since the surface azimuth (γ) = 0o

The zenith angle (θz) can be found setting the slope (β) equal to zero in this equation. With the zenith angle found, the solar azimuth angle (γs) can be calculated as follows:

γs = sign(ω) |cos-1 [ (cosθz sinΦ – sinδ) / (sin θz cosΦ) ] |[6]

## Example Calculation

Question:

Kingston, Ontario is located at 44.1oN, 76.3oW, roughly 100m above sea level. For a 4m2 collecting surface orientated directly south and tilted 45o, find the incident beam radiation at 10:30 (solar time) on February 13th.

Solution:

For the given scenario,

Angle of Declination (δ) = 23.45 sin[ 360 (284 + n) / 365 ] = - 13.95o

Hour Angle (ω) = (-2.5)(15) = - 22.5o

Surface Azimuth (γ) = 0o

Slope (β) = 45o

Latitude(Φ) = 44.1o

Applying,

cosθ = sinδ sinΦ cosβ – sinδ cosΦ sinβ cosγ + cosδ cosΦ cosβ cosω + cosδ sinΦ sinβ cosγ cosω + cosδ sinβ sinγ sinω

We get angle of incidence, θ = 25.8o

Next,

The air mass is AM = 1 / cos (-22.5) = 1.08

The incoming beam radiation is then calculated:

ID = 1.353 [ (1 - 0.14h) 0.7(AM^0.678) + 0.14h]

ID = 0.935 kW/m2 (IG = 1.03 kW/m2)

Finally, for θ = 25.8o, the beam radiation intercepted by the surface is

(ID)(cosθ)(Area)

(935 W/m2) (cos25.8o) (4m2) = 3367 W

Therefore, for the given location, time and collector orientation the total intercepted radiation is 3367 W. The actual energy utilized however will depend on various collector parameters and system conditions.

Shading can be caused by nearby obstructions such as buildings, overhangs or other collectors in an array. This can have a drastic impact on system performance, particularly for solar PV panels and it is therefore important to consider when and for how long shading will occur and determine if it is avoidable through design measures.

Obstructions can have irregular geometries and be located anywhere in relation to collector surface. By calculating their relative azimuth and altitude angles, a shading profile can be established by overlaying this information onto a solar chart (a solar chart is a graph used to plot the sun's position throughout the year for a given latitude). Figure 5 provides an example of theoretical solar chart and shading profile, where the darkened areas represent when shading will occur. For example, we can read off the chart that the collector will be shaded on October and February 21st between 9:30am and 11:30am and between 2:00pm and 4:30pm.

# Measuring Solar Resource

In addition to providing important meteorological data, measuring solar radiation provides valuable data sets that can be used for modeling and feasibility studies. In field testing of panels also requires accurate monitoring of radiation values. There are three main types of measurement devices[7]:

PyrheliometersW
• Measures beam radiation by targeting a small portion of the sky around the sun
• Typically induce a temperature fluctuation onto an enclosed target
• Requires tracking of the sun
PyranometersW
• Measures beam + diffuse radiation (or diffuse only) using a semi-spherical chamber
• Device typically operates by utilizing thermopile circuit across selective surfaces
• Number of models available offering varying degrees of accuracy
PV detectors
• Spectrally responsive detector
• Calibration constants available to account for remaining spectrum, however these are unreliable due to variations in actual spectral distribution
• Relatively Inexpensive

A more comprehensive review of solar radiation measurement devices and techniques can be found here.

For all radiation measurement devices, a number of factors determines the overall quality and accuracy of retrieved data:

Glass Layer
For devices that require an external glass layer, the uniformity of the thickness in this layer is extremely important to avoid refractive effects. The glass should have very low reflective properties.
Moisture Content
Any moisture within the measurement zone can skew the incoming radiation via reflection and refraction. In addition to proper sealing a number of devices use a replaceable solid desiccant to ensure dry conditions inside the device.
Temperature Sensitivity
The response of the circuitry used to output data can vary with temperature fluctuations induced by exposure to radiation and ambient temperature changes. It is difficult to thermally isolate these circuits, however a number of devices use multiple junctions or temperature compensation factors to minimize this effect.
Orientation
The semi-spherical chamber used in pyranometers does not maintain a perfect vacuum. As a result, if the device is used to measure radiation on a tilt angle, the heated air inside the chamber can form convective currents which can induce further issues associated with temperature sensitivity and radiation interference.
All measurement device degrade over time. It is recommended that calibration constants for be re-evaluated every few years to ensure accurate readings.

In addition to ground-based measurements, data can also be inferred from satellite observations of the atmosphere. NASA provides monthly radiation data sets for a number of locations across the globe using meteorological data and satellite observations. This data provides a convenient source for performing preliminary feasibility studies, however should only be used if ground-based data is not available[8]. Table 3 highlights the uncertainties associated with measured radiation data.

Table 3: Uncertainty in Radiation Data[9]
Data Source Uncertainty
NASA Data Set 7 - 12%
Ground-Measured 6 - 12%
Ground-Measured by High Quality Research Sites 3 - 6%

# Simulating Performance

Modelling provides a tangible way of predicting performance for a variety of system configurations and environmental conditions. To verify a models validity, a number of well defined scenarios are simulated and compared to experimental data. If the simulated results are adequately close to the experimental results, the model is validated to a specific degree of accuracy based on the data differential. Alternatively, newly developed models are often validated against existing models which have already been validated.

A number of simulation tools are available to model various system configurations. The most basic simulation program must provide inputs for radiation data, collector characteristics and collector orientation; and perform monthly,daily or yearly calculations similar to what has been demonstrated in the example provided earlier.

Beyond these inputs, a number of simulation tools provide additional inputs to better define the system being modeled. Inverter characteristics, battery information, pump characteristics, wiring information, piping information, system energy demand, energy prices, and wind conditions are some examples of inputs that would provide greater flexibility and detail. Some tools are also streamlined to specifically simulate a small range of system types and provide easy to use outputs.

A list of PV simulation tools and a general description can be found here. The simulation tool RETScreen is discussed in further detail below.

## RETScreen

Figure 6: RETScreen PV Energy Models

RETScreen is a free renewable energy technology analysis tool (solar, wind, biomass, hydro, etc.) developed by CanmetEnergy of Natural Resources Canada in collaboration with a number of other government and multi-lateral organizations.

The program works as a plug-in for Microsoft Excel 2000 or higher and includes a built in monthly radiation database from NASA. Simulations can performed for a variety of PV panel types (a-Si, c-Si, etc.) and allows the user to select one of three system types: On-Grid, Off-Grid or Water Pumping model. Figure 6[10] shows the data processing schematic for each type.

In addition to calculating energy production and emissions reduction, RETScreen also accepts inputs for electricity, system component, labor and maintenance costs. Utilizing these inputs and user defined inflation and interest rates and leveraged percentage, the simulation provides an analysis to determine the its financial viability.

Limitations

While RETScreen is a useful tool for system analysis it is subject to a number of limitation listed below.

Inherent to Program:

• Currently cannot model concentrator systems
• Cannot adequately customize system configuration
• Cannot compare configurations
• Only provides option to use monthly averaged radiation data (cannot utilize higher resolution ground-measured data)
• Does not provide reliability measure (loss of load probability)

User Controlled:

• Financial analysis easy to manipulate for ideal findings

Given the above limitations, RETScreen remains a valuable tools for preliminary feasibility studies. Findings, however, should be presented with a sensitivity analysis in order to provide some insight to the variability in performance and cost recovery. Once project specifications are known in greater detail, RETScreen results should be complimented with more detailed analysis tailored specifically to the proposed project in order to account for hourly radiation fluctuations, shading, etc.

The PVCDROM is an online educational tool developed by Stuart Bowden and Christiana Honsberg who work at the Solar Power Labs at Arizona State University. The content includes solar energy fundamentals and information on photovoltaic technology.

CanmetEnergy is subsidiary of Natural Resources Canada. Their website hosts information on renewable technologies, including solar PV and solar thermal technologies.

The Appropedia page photovoltaics provides a technical overview of all the components in a solar PV system.

The Solar Photovoltaic Open Lectures is a series of five fully annotated slide presentations created for the solar energy community to assist in the dissemination of information about solar photovoltaic (PV) cells.

# References

1. Duffie J. A., Beckman W. A., Solar Engineering of Thermal Processes, pp7, John Wiley & Sons Inc, 2006
2. Hu, C. and White, R.M., "Solar Cells: From Basic to Advanced Systems", McGraw-Hill, New York, 1983
3. Honsberg C., Bowden S., Photovoltaics DROM, Properties of Sunlight, http://pvcdrom.pveducation.org/index
4. Duffie J. A., Beckman W. A., Solar Engineering of Thermal Processes, pp13, John Wiley & Sons Inc, 2006
5. Duffie J. A., Beckman W. A., Solar Engineering of Thermal Processes, pp14, John Wiley & Sons Inc, 2006
6. Duffie J. A., Beckman W. A., Solar Engineering of Thermal Processes, pp16, John Wiley & Sons Inc, 2006
7. Duffie J. A., Beckman W. A., Solar Engineering of Thermal Processes, pp44-49, John Wiley & Sons Inc, 2006
8. Stackhouse W. P., Whitlock C. H., Surface meteorology and Solar Energy – Accuracy, NASA, 2010, http://eosweb.larc.nasa.gov/cgi-bin/sse/sse.cgi?+s05#s05
9. Stackhouse W. P., Whitlock C. H., NASA Derived and Validated Climate Data for RETScreen Use: Description and Access, NASA Langley Research Center, 2008, www.RETScreen.net/fichier.php/1365/NASA_Data.ppt
10. Natural Resources Canada, Photovoltaic Project Analysis, RETScreen International, 2010, http://www.retscreen.net/ang/course_pv.html

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## Precalculus: Mathematics for Calculus, 7th Edition

a.) -3 b.) $\frac{1}{2}$ c.) -1
$Evaluate$ $the$ $expression:$ a.) $\log_3 (\frac{1}{27})$ b.) $\log_{10} \sqrt{10}$ c.) $\log_5 0.2$ a.) $\log_3 (\frac{1}{27})$ Rewrite $\frac{1}{27}$ as $3^{-3}$ [Note: $3^{-3} = \frac{1}{3^3} = \frac{1}{3\times3\times3} = \frac{1}{27}$] $\log_3 3^{-3}$ Use the Third Property of Logarithms: $\log_a a^x = x$ $\log_3 3^{-3} = -3$ b.) $\log_{10} \sqrt{10}$ Rewrite the root to exponential form: $\sqrt{x} = x^{\frac{1}{2}}$] $\log_{10} 10^{\frac{1}{2}}$ Use the Third Property of Logarithms: $\log_a a^x = x$ $\log_{10} 10^{\frac{1}{2}} = \frac{1}{2}$ c.) $\log_5 0.2$ Rewrite 0.2 as $5^{-1}$ [Note: $5^{-1} = \frac{1}{5} = 0.2$] $\log_5 5^{-1}$ Use the Third Property of Logarithms: $\log_a a^x = x$ $\log_5 5^{-1} = -1$


text:
# 10.9. Vector of random numbers¶

The first step is to generate a large number of random values and store them in a vector. By “large number,” of course, I mean 20. It’s always a good idea to start with a manageable number, to help with debugging, and then increase it later.

The following function takes a single argument, the size of the vector. It allocates a new vector of ints, and fills it with random values between 0 and upperBound-1.

vector<int> randomVector (int n, int upperBound) {
vector<int> vec (n);
for (size_t i = 0; i < vec.size(); i++) {
vec[i] = random () % upperBound;
}
return vec;
}

The return type is vector<int>, which means that this function returns a vector of integers. To test this function, it is convenient to have a function that outputs the contents of a vector.

void printVector (const vector<int>& vec) {
for (size_t i = 0; i < vec.size(); i++) {
cout << vec[i] << " ";
}
}

Notice that it is legal to pass vectors by reference. In fact it is quite common, since it makes it unnecessary to copy the vector. Since printVector does not modify the vector, we declare the parameter const.

The following code generates a vector and outputs it:

int numValues = 20;
int upperBound = 10;
vector<int> vector = randomVector (numValues, upperBound);
printVector (vector);

On my machine the output is

3 6 7 5 3 5 6 2 9 1 2 7 0 9 3 6 0 6 2 6

which is pretty random-looking. Your results might be different.

Try running the active code below!

If these numbers are really random, we expect each digit to appear the same number of times—twice each. In fact, the number 6 appears five times, and the numbers 4 and 8 never appear at all.

Do these results mean the values are not really uniform? It’s hard to tell. With so few values, the chances are slim that we would get exactly what we expect. But as the number of values increases, the outcome should be more predictable.

To test this theory, we’ll write some programs that count the number of times each value appears, and then see what happens when we increase numValues.


text:
# Converting Earth Moon Barycenter coordinate to Geocentric coordinate

I have Earth Moon Barycenter coordinate (J2000) generated from VSOP2013 in Astronomical Units,

JD=2415020.5
X=-0.1968857640    Y=0.9633224602     Z=0.0002147057    AU
X'=-0.0171376156   Y'=-0.0035078892   Z'=-0.0000011481  AU/day

How to convert it to Geocentric?

• Find the coordinates for the Earth's barycenter and subtract. Note the Earth-Moon barycenter actually lies about 1000 miles below the Earth's surface, since the Earth is about 81 times more massive than the Moon. – user21 Jul 27 '17 at 14:32


text:
Free Version
Easy

# Degrees of Freedom

APSTAT-ZDXXJS

What is an appropriate number of degrees of freedom to use when conducting a two-sample $t$-test for the difference between two means?

A

$n – 1$, where $n$ is the number of different populations.

B

$n – 1$, where $n$ is the larger of the two sample sizes.

C

$n – 1$, where $n$ is the smaller of the two sample sizes.

D

$n – 1$, where $n$ is the total number of observations in both samples combined.

E

$n – 2$, where $n$ is the total number of observations in both samples combined.


text:
• Definition for "conceptualisation"
• the work of conceptualising, or something like that…
• Sentence for "conceptualisation"
• Although the latter is of more…
• Synonym for "conceptualisation"
• conceptualization
• Same Context for "conceptualisation"
• patchup

# conceptualisation definition

• noun:
• the work of conceptualising, or something like that conceptualised
• the act of formulating or making a concept of one thing.
• an elaborated concept
• inventing or contriving a notion or explanation and formulating it psychologically