So I came across two similar questions on ADAPT which use two different methodologies to solve and I am not sure why.
One question gives a list of monthly stock prices and asks to estimate the sharpe ratio.
In order to do this, r is given so we need to find a and sigma.
I use the TI multiview calculator way to solve this and get the x(bar) and sx.
From what I understand, sx is the monthly volatility and x(bar) is the same as mu(bar) in the following equation:
alpha(hat) = mu(bar)/h + delta + (sigma(hat)^2)/2
For the first value, I just divide the x(bar) by 1/12 since it is monthly and I multiply sqrt(12) to sx and then square it to get the annual variance and divide it by two to get the last value in the formula.
This all makes sense to me but I came across another question that asked to estimate the continuously compounded expected rate of return on the stock given monthly closing prices on nondividend stock.
Here, instead of multiplying the volatility by sqrt(12) and then squaring, it just multiplies it by 12(divide by h, which is 1/12) to get the annual alpha.
alpha=(r(bar)+(sigma^2)/2)/h
When I compare the equation to that of above, the r(bar) is the same as mu bar in the first equation (I don't know why they use different terms), but the second value that deals with volatility is not the same.
In the first equation the second part is [(monthly volatility*sqrt(12))^2]/2.
But the second equation has the second part as [(monthly volatility^2)*12]/2
Why are they different?
One question gives a list of monthly stock prices and asks to estimate the sharpe ratio.
In order to do this, r is given so we need to find a and sigma.
I use the TI multiview calculator way to solve this and get the x(bar) and sx.
From what I understand, sx is the monthly volatility and x(bar) is the same as mu(bar) in the following equation:
alpha(hat) = mu(bar)/h + delta + (sigma(hat)^2)/2
For the first value, I just divide the x(bar) by 1/12 since it is monthly and I multiply sqrt(12) to sx and then square it to get the annual variance and divide it by two to get the last value in the formula.
This all makes sense to me but I came across another question that asked to estimate the continuously compounded expected rate of return on the stock given monthly closing prices on nondividend stock.
Here, instead of multiplying the volatility by sqrt(12) and then squaring, it just multiplies it by 12(divide by h, which is 1/12) to get the annual alpha.
alpha=(r(bar)+(sigma^2)/2)/h
When I compare the equation to that of above, the r(bar) is the same as mu bar in the first equation (I don't know why they use different terms), but the second value that deals with volatility is not the same.
In the first equation the second part is [(monthly volatility*sqrt(12))^2]/2.
But the second equation has the second part as [(monthly volatility^2)*12]/2
Why are they different?
Solving for a and volatility given list of stock prices