Performance Appraisal: Capture Ratios
Obviously, you want your money managers to beat their benchmarks.
If a manager could promise 110% of benchmark returns, would that be a win?
Not necessarily.
Good answer!
It depends on if that's 110% of a good return, or 110% of a bad return. Without separating those two scenarios, you're just talking about some simple leverage.
What really speaks to managers' skills is how they do when markets are moving in certain directions. In which market environment would you want the manager's portfolio returns to be closer to zero relative to the benchmark?
Not true. In some environments, zero sounds great.
No, that's not right; that would just mean underperformance.
Exactly. So the upside capture (UC) ratio measures how much of an "up" return ($$R$$) in the benchmark ($$B$$) is captured by the manager ($$m$$), which is hopefully 100% or more. The downside capture (DC) ratio measures how much "down" movement is captured by the manager (hopefully less than 100%). Here are the expressions.
>$$ UC(m,B,t) = \frac{R(m,t)}{R(B,t)} \text{ if } R(B,t) \geq 0 $$
>$$ DC(m,B,t) = \frac{R(m,t)}{R(B,t)} \text{ if } R(B,t) \lt 0 $$
Suppose the benchmark returned 2.8% and the manager earned 2.1% in the first period. Where would this go?
Sure. This is a positive return, so it's part of upside capture. And is this good news or bad news for the manager?
Actually, no; this is a positive return, so it's part of upside capture. And is this good news or bad news for the manager?
It's actually not.
Right again!
The manager underperformed relative to the benchmark, just capturing 75% of the gain. Here are a few more returns to illustrate the process through five periods:
| Period | Manager Return | Benchmark Return |
|-----|-----|-----|
| 1 | 2.1% | 2.8% |
| 2 | 0.4% | 1.3% |
| 3 | -1.2% | -0.8% |
| 4 | 0.9% | 0.4% |
| 5 | -2.9% | -2.1% |
Start with upside capture. How many periods will you need to deal with?
There you go, yes.
Perfect. There are three positive portfolio returns, so that's what will be used for the upside capture.
No, it's 3. There are three positive portfolio returns, so that's what will be used for the upside capture.
You just need the geometric mean (GM) return for each in order to make the ratio, and you're done. For the manager, these three returns provide a mean return of:
>$$ GM_m = \left[ (1 + 0.021)(1 + 0.004)(1 + 0.009) \right]^{(1/3)} - 1 = 1.1308 \%$$.
Do the same for the benchmark portfolio. What is its GM return?
About that, yes. But always keep some extra significant digits to be safe.
>$$ GM_B = \left[ (1 + 0.028)(1 + 0.013)(1 + 0.004) \right]^{(1/3)} - 1 = 1.4952 \% $$
Then the upside capture (UC) is the ratio of these two GM returns:
>$$\displaystyle UC = \frac{1.1308 \%}{1.4952 \%} \approx 75.6 \%$$.
How did the manager do in upside markets?
Incorrect.
Not really.
You're right.
The manager only "captured" 75.6% of market gains, so investors would have been better off with an index fund. Now try the downside capture ratio with the other two periods. What ratio do you find, as a percentage?
Excellent!
Not quite; can you tell whether it's over or under 100%?
That's okay. It's actually over 100%.
That's right!
No, actually over 100%.
You can tell it's over 100% because the manager suffered worse losses than the benchmark in both down periods. So the manager more than captured these losses, unfortunately. The calculations are as follows.
>$$ GM_m = \left[ (1 - 0.012)(1 - 0.029) \right]^{(1/2)} - 1 = -2.0537 \% $$
>$$ GM_B = \left[ (1 - 0.008)(1 - 0.021) \right]^{(1/2)} - 1 = -1.4521 \% $$
>$$\displaystyle DC = \frac{-2.0537 \%}{-1.4521 \%} \approx 141.4 \% $$
This is leads to a concave manager return as a function of benchmark return: lower positives and higher negatives. So this is clearly not good performance. What you want to see is a convex profile: better in good times, better in bad times.
Better luck next time!
To summarize:
[[summary]]
No
Yes
Maybe
None
In an up market
In a down market
Upside capture
Downside capture
Good news
Bad news
Good news
Bad news
3
Other responses
Other responses
1.495
1.5
Good
Not good
Other responses
141
No
Over 100%
Under 100%
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