I would appreciate if you could help me with this. It looks very simple but is confusing to me.
If your fund’s cumulative return is 40.4% and your benchmark’s cumulative return is 5.5%, which expression is correct? The fund outperformed the benchmark by 634% or by 34.9%.
If your fund’s annualized volatility is 8.5% and the benchmark is 16.1%, can you say that your fund took 53% of risk?
Is it right that your fund outperformed the benchmark by 634% taking on 53%? Or do you give your fund’s annualized return instead of annualized return to give annualized volatility?
Is it right that your fund outperformed the benchmark by 634% taking on 53%? Or do you give your fund’s annualized return instead of cumulative return to give annualized volatility?
Generally, you say that your fund outperformed the benchmark by 34.9%. That’s because if you invest $100 in the fund, you’ll get 5.5% from your benchmark by the end, and you’ll get 34.9% more than that by being in your fund. Yes, there is a mathematical argument about why you can say it’s 634%, but most people just want to know how much more money they have at the end than what they started with, and the 34.9% tells you that in a straightforward way. And you will be signaling to your client that they have to be very careful about trusting your numbers and the small print in your text about how you compute them if you use the 600% figure. With respect to risk, it depends a little on the context, but you can say that the fund has about half of the risk of the benchmark, although it’s worth pointing out that this is half of the volatility risk… there are risks that don’t always show up as volatility, especially things like counterparty risk or default risk. There are also times when you want to break down the risk into how much comes from exposure to the benchmark and how much comes from your active decisions to depart from the benchmark.
A) 34.9% B) Just say the fund is about half as volatile as the benchmark (and cite the stats) C) Use the same framing across the board. To do otherwise is boderline unethical, and would never be approved for outside use.
BTW, point #3 is why you ultimately need to rely on risk-adjusted return measures like Sharpe Ratio, Information Ratio, Treynor Ratio. A reasonable way to say it is that the fund gave 34.9% more return on your investment than the benchmark, with about half the risk. The Sharpe Ratio of the fund (assuming a RFR=1%) is 4.6, vs a benchmark Sharpe Ratio of 0.5. This implies that the fund is about 9x more effective in its use of risk than the benchmark (although an investor immediately needs to ask themselves what kinds of risks are not showing up in the volatility measures before committing substantial capital).
relative return is always a relative number. not a ratio. also, if you want to measure risk against a benchmark, just use the tracking error figure. and additionally, take the excess return over tracking error which will give you the information ratio for a straight forward look at excess return per unit of risk.
Depending on the fund’s style, tracking error may not be appropriate. I actually dislike tracking error since it rewards PMs for basically running an enhanced indexed fund. Now, if that’s your style - institutionally managed, minimal factor bets - then tracking error and IR are what you want to use, and a good indicator of the value added by the manager. However, if your fund takes large factor bets - huge sector bets, any sort of bias like size, volatility, momentum, etc. - or if you run a concentrated portfolio - Alpha (benchmark aware) and Sharpe (not benchmark aware) might be more appropriate than IR.
Well, the information ratio is still relevant even if you are taking large bets, and that requires taking a look at tracking error. However, if you are going to be allowed to make large departures from a benchmark, then it may be more appropriate just to use cash as your benchmark and look at the Sharpe ratio, or look at the Treynor ratio to see how much return you are getting, compared to an equivalent amount of market risk. I like how this question brings out interesting answers.
Remember, you can breakdown the true risk and misfit risk. But to the point, if you are taking large bets as reflective to the benchmark, then in reality, that particular benchmark is not representative and another benchmark should be chosen. Treynor should not be applicable as it’s against Beta risk. You really want the total risk or the True risk here.
Tracking error is only appropriate when you closely adhere to a benchmark. Take Fairholme for example. (Let’s forget that it’s completely sucking this year.) It’s in the large value space right now, so should you use the R1000 Value index as the benchmark? Well, probably not since three years ago Fairholme was more of a growth fund. Cash wouldn’t be appropriate since the fund would take up part of your equity allocation. You’re pretty much forced to use the S&P 500. But, by definition of what Fairholme does, they’ll have huge tracking error all the time. It’s better to look at Alpha in this scenario because your alternative is buying the broad market. If you compare a fund like Fairholme to a more benchmark aware alternative, IR could very well steer you in the wrong direction. A fund with 4% excess return and 2% tracking error looks like an all-star (and would be actually), but Fairholme may have 6% excess return with 10% tracking error. Now, if we’re talking about a portfolio that can short, then cash may be more appropriate, though still far from perfect. Does the investor “feel” tracking error like you do volatility/std dev? I’d argue no. But that just brings us to a conversation about what risk is. Interestingly as I previewed my post I realized something. While investors may not feel tracking error like they do volatility, the high tracking error of a fund like Fairholme was exactly why they suck this year. In that respect, tracking error was a good indicator of risk. I just had a conversation with myself. I need a beer.
I prefer 3 factor regression in these types of style drift senarios. The y-intercept gives you an alpha regardless of drift and you also get a standard error so you can assign a confidence level.