Sharp Ratio from monthly returns industry, internet, standard, monthly, returns

eagles_dare13

Is there an industry standard for calcing the sharp ratio from monthly returns? Looking around the internet I have seen quite a few variations.

king_kong

You could calculate it from any frequency, but the trick is when taking it from your frequency to an annual basis (which I think is how most people would compare things to one another).

If returns are normally distributed and there's no serial correlation, you can multiple the sharpe ratio by (f_end/f_begin)^0.5 to get an approximation of the annualized value, where f_end is the end frequency and f_begin is the beginning frequency (normally 1 initially).

ayaz_mahmud369

Bill Sharpe usually likes to have an "e" at the end of his ratio. ;-)

The other question that comes up a lot is what to use for the risk-free rate. The answer is to use the treasury yield that has the same maturity as your holding period. So this actually suggests that the Sharpe Ratio may differ depending on the client and their holding period.

In practice, long-term historical studies often compare equity returns to 10-year bond yields because those are suitable comparables for people who are investing for long time horizons. However, active strategies will often set it to the 90-day T-bill because they are rebalancing and adjusting their portfolios on a quarterly or monthly basis (or even faster). This is defensible, but I suspect people really like to use the 90-day T-bill because it increases the resulting Sharpe Ratio (since the 90d T-bill is usually a lower yield than the 10 year note).

tobeornottobe

Hmmmm, is that really the case?

At a minimum, you wouldn't want to subtract the average 10-year bond yield. Presumably, you would want to subtract the total return on an investment that regularly rolled over 10-year bonds. You're only accounting for the yield return and not the duration impact.

Further, if you're benchmarking yourself against a 10-year Treasury, you'd want to incorporate it in the standard deviation so it's more like an information ratio. The Sharpe ratio doesn't incorporate the risk-free rate in the standard deviation because it presumably has a 0 standard deviation.

The reason a T-bill at the short end is because there is essentially no duration and it is almost certainly risk-free over that horizon.

I sort of see your point, in that if you invest for ten years, you could have purchased a 10 year bond on day 1 and went to sleep and woke up ten years later and that's your risk-free return. The 90-day rate has reinvestment risk. However, that's not the same thing as the average 10-year bond yield over that period. Further, it would only work if you have bootstrapped the yield curve at inception, found the zero coupon yield over the period where you want to evaluate the Sharpe ratio, and use that. If you're horizon is 10+ years, there are fewer points to bootstrap and your zero coupon yield would have some estimation error.

random_walker47

I was just bringing up that there is a longstanding debate about what RFR to use, and that the only agreement seems to be that if you specify an investment horizon, the RFR is the rate on a zero coupon Treasury security that matures at the same time as that investment horizon.

It also implies that, unless the yield curve is perfectly flat, the Sharpe Ratio will actually be different for different investors, because of their different time horizons.

If my investment horizon is 10 years, then the 90d T-bill is in fact quite risky, because I have reinvestment risk. 90d T-bill interest rates can wander all over the place in the interim. If my horizon is 1 year, then the 10y note is very risky because it has a ton of interest rate risk. It's really only the zero-coupon bond maturing at the right time (or possibly a regular coupon treasury with the same duration) that is risk free. Then you can have more fun by asking about inflation adjustments.

In the mutual fund world, most managers don't necessarily know what the investor's time horizon is, because everyone might have a different one, so there it makes sense to make the RFR equal to a typical holding/rebalancing period, and usually that means either the 90d Treasury or the 1y treasury. In long term asset allocation studies for retirement planning, the 10y Treasury average yield may make more sense, although some people will might adjust those allocations yearly depending on where the 10y has gone in the interim. If your risk taking ability is constant, then changing interest rates will affect your division between cash and risky assets, although it might be small, especially if the Sharpe ratio is small.



Edited 2 time(s). Last edit at Thursday, May 19, 2011 at 09:08PM by bchadwick.

dmrktrading

I should add that I usually use rolling 90 day T-bill yields (laddered 30-60-90d) as my estimate for RFR. It has the benefit of being defensible; gives higher ratios for marketing purposes, and cash sitting in the bank earning 90d yields really is kind of the default position for "I'm too scared to invest anything and I don't have any other ideas," which would be what you do when you don't want to take any risk.

However, if you are investing against a known set of liabilities, then you do have a known time horizon (basically the combined duration of those liabilities), and from there you can figure out what your RFR should be.

mik82

We use 3mo LIBOR in the applicable currency as the risk free rate ($50bn+ asset manager)

Andreas42

I've seen 3 month LIBOR used widely. I think BChadwick has hit on the two main reasons:

1. It tends to improve the reported Sharpe ratio.
2. It is defensible if a client queries it.