# Tag Info

## Hot answers tagged return

6

### Square root of time

Scaling volatility as you do is often leading to inaccurate results which is over-estimating volatility especially when you scale daily volatility to even longer periods. Please see the following for more: http://economics.sas.upenn.edu/~fdiebold/papers/paper18/dsi.pdf The above paper also explains why scaling the way you did does not properly account for ...

2

### Regression giving the return on a stock

The basic CAPM - which is what your regression estimates - says $$R_S = R_f + \beta_S (R_{Market}-R_f)$$ where $$\beta_S = \frac{Cov(R_M,R_S)}{Var(R_M)}$$ i.e. the return of a certain stock depends only on the correlation with the market portfolio. For your pricing equation to work, you will need to have an idea about the expected market (excess) ...

1

### Calculating Geometric mean

I'm currently also using daily returns which I want to annualize. This is my approach: For every month, I calculate the simple return using the formula: (end-of-month closing price / beginning-of-month closing price) - 1. I use the Excel formula somproduct(geomean(A1:A12+1)-1) to find the monthly compounded return. Finally, I annualize the result of step 2 ...

1

### Square root of time

for the square-root rule: it holds for log-returns, if you assume the same variance and no autocorrelation. Because then: $$Var[r_1 + \cdots + r_d] = Var[r_1] + \cdots + Var[r_d] = d Var[r_1]$$ and thus $$\sqrt{Var[r_1 + \cdots + r_d] } = \sqrt{d} \sqrt{Var[r_1]}.$$ This is mathematically true for any distribution that fulfills the assumptions. For the ...

1

### Logarithmic returns for realized variance?

It depends on your investment strategy. The most common approach is to use the close price of $p_t$ and $p_{t+1}$. The volatility you measure using this method implies the "assumption" that your are able to trade at close every day. If you choose to compute the daily returns from open to close, then you assume that you are selling your position every night ...

1

### Is Arithmetic Return Bias Basis of Low Vol Anomaly?

No, the "low-beta" anomaly is not the result of the difference between arithmetic and geometric mean returns. Statistical tests verifying the existence of the anomaly rely on models employing the arithmetic mean returns, $$\mu_a = \mu_g + \frac{\sigma^2}{2}$$, hence the penalty excess volatility incurs when compounding returns over time does not explain the ...

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