# not too sharpe about ratios

March 14, 2006 4:39 PM Subscribe

I don't understand Sharpe Ratios and the results I'm getting in my Excel document of a fund's returns.

I'm helping out some family with an Excel document of a hedge fund's returns. The equations I have based on Sharpe Ratios are not working out. First of all, I need to calculate the annualized Sharpe Ratio for this fund. The equation I am using is:

(annualized average for the year - risk free rate) / annualized standard deviation

Is this correct, for starters?

Secondly, about that risk free rate. What is it, and how do I get one? (Is it something that is looked up, or calculated?) How often does it change? Does, say, the fund return for April 2004 use an April 2004 RFR, or do past months' performance get analyzed based on whatever the current RFR is?

Thirdly, about knowing what the results should look like: should my resulting Sharpe ratios tend to be positive numbers? How can I tell if my results are in the right ballpark?

I'm helping out some family with an Excel document of a hedge fund's returns. The equations I have based on Sharpe Ratios are not working out. First of all, I need to calculate the annualized Sharpe Ratio for this fund. The equation I am using is:

(annualized average for the year - risk free rate) / annualized standard deviation

Is this correct, for starters?

Secondly, about that risk free rate. What is it, and how do I get one? (Is it something that is looked up, or calculated?) How often does it change? Does, say, the fund return for April 2004 use an April 2004 RFR, or do past months' performance get analyzed based on whatever the current RFR is?

Thirdly, about knowing what the results should look like: should my resulting Sharpe ratios tend to be positive numbers? How can I tell if my results are in the right ballpark?

You won't know the volatility of the underlying portfolio so you won't be able to calculate the Sharpe ratio. You might also argue that for a hedge fund you would need to ask your self return volatility compared to what? What sort of risk am I paying them to not take? Also it makes no sense to look at monthly return volatility.

Finally you don't want T-bills as the RFR - you want the longest dated gov't paper you can find - probably a ten-year.

Most importantly remember return volatility is not equal to risk.

If you are really paying 2 and 20 for a hedge fund you should be using alpha measurement tools far more sophisticated then a sharpe ratio.

posted by JPD at 5:28 PM on March 14, 2006

Finally you don't want T-bills as the RFR - you want the longest dated gov't paper you can find - probably a ten-year.

Most importantly remember return volatility is not equal to risk.

If you are really paying 2 and 20 for a hedge fund you should be using alpha measurement tools far more sophisticated then a sharpe ratio.

posted by JPD at 5:28 PM on March 14, 2006

Response by poster: Please note, because the first answers I have gotten lead me to think it matters: I am not, and no one I know is

posted by xo at 5:34 PM on March 14, 2006

*investing*in this fund. I still need to figure out this Sharpe Ratio business.posted by xo at 5:34 PM on March 14, 2006

What part of the sharpe ratio are you having difficulty with?

RFR= 10 year treasury

Formula is correct

Do you understand the concept behind the ratio? Trade-off between risk and return - with 1 being an efficient portfolio? BTW - you should be measuring returns after fees?

If its not for an investment might I ask what you are up to? I might be able to suggest a different methodology.

If they are good funds the Sharpe ratio should be positive, with best 1 or better. But they could just as easily be negative.

posted by JPD at 5:45 PM on March 14, 2006

RFR= 10 year treasury

Formula is correct

Do you understand the concept behind the ratio? Trade-off between risk and return - with 1 being an efficient portfolio? BTW - you should be measuring returns after fees?

If its not for an investment might I ask what you are up to? I might be able to suggest a different methodology.

If they are good funds the Sharpe ratio should be positive, with best 1 or better. But they could just as easily be negative.

posted by JPD at 5:45 PM on March 14, 2006

Your Sharpes will be positive numbers if the fund's beating the RFR. Sharpes over 1 are "good". Sharpes less than 1 are "bad" - you're not getting enough return for the amount of risk you're taking. When I worked at a fund of funds place, we used the 91 day T bill rate for our RFR. JPD's right - your standard deviation is unknown, so any Sharpe will have very little informative value.

This is what I'd do. I'd take 100 as your base, apply your monthly returns to it, and get to a value V. Do your V/100-1 to get your rate of return

posted by sachinag at 5:54 PM on March 14, 2006

This is what I'd do. I'd take 100 as your base, apply your monthly returns to it, and get to a value V. Do your V/100-1 to get your rate of return

*r*. Then use =stdev() on your monthly returns to get your standard deviation*s*. Take your return*r*, subtract your RFR (use 91 day T bill rate or the 10 year that JPD suggests or whatever) then divide by your*s*. That'll be your Sharpe ratio since inception.posted by sachinag at 5:54 PM on March 14, 2006

I'd love to hear how FoF try to measure risk given the opacity in the their holdings and the correlated holdings you can get with hedgies.

I always assumed it was sort of a facade.

posted by JPD at 6:04 PM on March 14, 2006

I always assumed it was sort of a facade.

posted by JPD at 6:04 PM on March 14, 2006

Depending on what the fund is doing, the Sharpe ratio is probably going to be a really poor measure of a risk/reward tradeoff, since the underlying distribution of the return series is likely going to be asymmetric.

posted by milkrate at 7:00 PM on March 14, 2006

posted by milkrate at 7:00 PM on March 14, 2006

For your purposes subtracting a constant risk free rate is fine, say 3%/year. If you are starting with monthly returns then the formula for annualized sharpe ratio will be =(average(returns)-(3%/12))/stdev(returns)*sqrt(12)

The sqrt(12) does the annualization, but if you are comparing a series of monthly returns, you dont need to do this (because the series with the highest monthly sharpe ratio will also have the highest annualized sharpe ratio.

The comments above suggest this is a highly simplistic way to look at hedge fund returns, and that is more or less true but what you are proposing is much better than doing nothing. What you really need to know is the effect your portfolio of hedge funds has on your overall portfolio. In the limit, if your portfolio outside of the funds was say 100% MSFT, then if a fund invested in MSFT that would not add any value to your portfolio. This brings us to the topic of correlation, which you might want to investigate on your own.

Failing a course in modern portfolio theory, a reasonable thing to do is put your whole portfolio (stocks, bonds, mutual funds, hedgefunds) into a spread sheet & see if the sharpe ratio goes up or down depending on whether or not the hedge funds are in there.

JPD: Hedge funds may be opaque to you, but they are not everyone. FOFs either explicitly (by asking) find out what their funds invest in or roughly figure it out (via the funds description of their investable universe and correlation of returns).

posted by shothotbot at 8:21 PM on March 14, 2006

The sqrt(12) does the annualization, but if you are comparing a series of monthly returns, you dont need to do this (because the series with the highest monthly sharpe ratio will also have the highest annualized sharpe ratio.

The comments above suggest this is a highly simplistic way to look at hedge fund returns, and that is more or less true but what you are proposing is much better than doing nothing. What you really need to know is the effect your portfolio of hedge funds has on your overall portfolio. In the limit, if your portfolio outside of the funds was say 100% MSFT, then if a fund invested in MSFT that would not add any value to your portfolio. This brings us to the topic of correlation, which you might want to investigate on your own.

Failing a course in modern portfolio theory, a reasonable thing to do is put your whole portfolio (stocks, bonds, mutual funds, hedgefunds) into a spread sheet & see if the sharpe ratio goes up or down depending on whether or not the hedge funds are in there.

JPD: Hedge funds may be opaque to you, but they are not everyone. FOFs either explicitly (by asking) find out what their funds invest in or roughly figure it out (via the funds description of their investable universe and correlation of returns).

posted by shothotbot at 8:21 PM on March 14, 2006

Actually I work on the investment side for a very large well established global long-short equity fund. So Hedge Funds are not opaque to me at all. My question was how do FoF attempt to manage risk given they never really know what the correllations across the different funds they are invested in.

I've seen the risk reports we send out. I have a pretty strong understanding of attribution analysis. There is no way you can get to what our holdings were during the quarter from that report. We aren't big traders so our 13F's are pretty realistic - but they don't include shorts.

If you own a stock slinger I don't see how you get to actually understand what sort of risk he is taking.

posted by JPD at 4:08 AM on March 15, 2006

I've seen the risk reports we send out. I have a pretty strong understanding of attribution analysis. There is no way you can get to what our holdings were during the quarter from that report. We aren't big traders so our 13F's are pretty realistic - but they don't include shorts.

If you own a stock slinger I don't see how you get to actually understand what sort of risk he is taking.

posted by JPD at 4:08 AM on March 15, 2006

I was going to take this offline but couldn't find your email. I will go put mine in my profile.

Obviously FOFs have the monthly returns of a big pile of funds, is your objection that the correlations of the individual funds will not be persistent? My intuition would be the opposite.

What I think is 1) the bigger guys do have some position level transparency (not that it does them any good because they have such long notice periods before they can get out). But more seriously 2) most of the people I talk to tend to do some high level portfolio construction based on style and sector then assume that with those groups people will do more or less the same. Say the have three categories: US small cap, european long short and convertible arb. They develop or buy some index of each sector and decide how much of each sector they want. Then they pick the individual managers on a more "qualitative" basis. In fact they will picking based on reputation and recent returns.

posted by shothotbot at 5:33 AM on March 15, 2006

Obviously FOFs have the monthly returns of a big pile of funds, is your objection that the correlations of the individual funds will not be persistent? My intuition would be the opposite.

What I think is 1) the bigger guys do have some position level transparency (not that it does them any good because they have such long notice periods before they can get out). But more seriously 2) most of the people I talk to tend to do some high level portfolio construction based on style and sector then assume that with those groups people will do more or less the same. Say the have three categories: US small cap, european long short and convertible arb. They develop or buy some index of each sector and decide how much of each sector they want. Then they pick the individual managers on a more "qualitative" basis. In fact they will picking based on reputation and recent returns.

posted by shothotbot at 5:33 AM on March 15, 2006

shothotbot's pretty much right. The big risk for a FOF is style drift - the risk of a long/short guy thinking he can play the global macro game, etc. etc. Our funds, when I worked there, had a rule that anything over some time frame (which I recall being semiannual redemption, but I could be wrong) wasn't allowed in.

The funds we owned were generally pretty decent about giving us some data on their holdings on a monthly basis - some gave us their whole portfolios, some gave us geographic/sector weights. That might have been a matter of size for us or just the fact that we had good relationships. I don't really know. We only really cared about the underlying assets individually if someone totally underperformed their style average.

posted by sachinag at 6:55 AM on March 15, 2006

The funds we owned were generally pretty decent about giving us some data on their holdings on a monthly basis - some gave us their whole portfolios, some gave us geographic/sector weights. That might have been a matter of size for us or just the fact that we had good relationships. I don't really know. We only really cared about the underlying assets individually if someone totally underperformed their style average.

posted by sachinag at 6:55 AM on March 15, 2006

I wanted to say that I appreciated the above comments. The perspectives are interesting and pertinent.

posted by ikkyu2 at 3:11 PM on March 15, 2006

posted by ikkyu2 at 3:11 PM on March 15, 2006

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2. The risk free rate would be the yield on a government bond. Wikipedia has articles on risk free rates and Sharpe ratios. The Fed posts T-Bill rates.

If the fund return is greater than the risk free return then the Sharpe ratio must be positive (standard deviations are always positive). It wouldn't be suprising if you got negative ratios for a hedge fund, given the volitility of their returns. Also, many hedge funds have minimum investment periods. This might complicate any calculations.

posted by thrako at 5:22 PM on March 14, 2006