Sharpe ratio

CFAI EOC # 23:

Magerski’s concern about a biased Sharpe ratio for hedge funds is most likely because:

1. eliminating extreme returns reduces the standard deviation of returns.
2. smoothing returns can overstate true gains and losses and calculated volatility.
3. lengthening the measurement interval from weekly data to monthly data increases the estimate of annualized standard deviation of returns.
I am confused. I picked C which is wrong. Why is it wrong?

In general, the longer the measurement interval, the lower the (annual) standard deviation: there’s a lot of noise in daily data that’s lost in weekly data, lots of noise in weekly data that’s lost in monthly data, and lots of noise in monthly data that’s lost in annual data.

Think of it this way: if you have 12 months of returns, you’ll (likely) have some positive standard deviation of returns; if you have 1 annual return you have zero standard deviation of returns.

Magician,

Your answer is not clear. I understand that longer the time interval, more volatile the retrun. What about other choices?

He’s saying the opposite. The longer the timeframe of measurement removes most noise (as S2000 call it) and the sample represents a more true depiction of the disturbution.

A) should be the answer as hedge funds exhibit negative skew and excess kurtosis. By removing the skew (remove the large outliers) you’re reducing the standard deviation of returns and likely understating risk.

B) should be wrong as smoothing returns reduces returns and losses, not increases

Hi Galli,

Thanks for your response. I have a q about the volatility and time. In option pricing, we learn that longer the time period, higher the volatility. Why here it is the opposite? A should be correct and resoning for B being wrong is correct. There is no confusion there.

Could you clarify?

It’s not the opposite.

You’re conflating the overall time period with the frequency of measurement.

The change in price for a year is greater than the change in price for a month (as you’d expect). But if you estimate the annual volatility with annual returns you’ll get get a lower number than if you estimate the annual volatility with monthly returns. Annual returns lose all of the intra-year volatility, but monthly returns capture some of that. Suppose that the price is \$100 in Jan, Feb, Mar, Apr, and May, then jumps to \$200 in June, then drops to \$110 in Jul, Aug, Sep, Oct, Nov, and Dec. The monthly returns will include a 100% increase in June, and a 45% decrease in July; the annual returns will show only a 10% increase for the year: much less volatile.

This is similar to bias you get in PE valuations, or real estate valuations which show low volatility due to the time frame between valuation periods being relatively large.

in short - greater the frequency of measurements - more volatility.

spread out the measurements - you SMOOTH your returns - and hence lower volatility.

Look at the graph of the bat flying (Pg 14-15 of the Capital Markets Expectation reading for reference) - goes in and comes out at almost the same level. But then look at the picture inside and see the various ups / downs / crashes it went through. Similar idea here.

Thanks guys. Its clear now.

My pleasure.