# Tag Info

6

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 ...

3

I'm guessing ${W_t^r}$ and ${W_t}$ correspond to real and nominal endowment at time $t$, respectively, and that ${P_t^g}$ is the price level at time $t$. In that case, $W_t^r \equiv W_t/P_t^g$ follows, and if endowment grows at a nominal interest rate $R_t$, then $W_t = W_{t-1}(1+R_t)$. We can write $W_{t-1}=(W_{t-1}^rP_{t-1}^g)$, so by substitution ...

1

I think there are 2 approaches being a bit mixed up here. You can analyze the option market by looking at implied volatilities and apply Black-Scholes (BS), thus assuming that log-returns follow a Gaussian distribution. Implied volatilies are the parameters that bring together BS and market prices. Then you will observe a pattern of implied volatilies for ...

1

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

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 ...

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