8.2 Performance Measures

Question 1

Sharpe ratio vs Treynor ratio:

Both calculated typically over 1, 3 and 5 years.

SR -> realised yearly … (whatkind of risk?)

TR -> realised yearly … (… risk)

Answer 1

outperformance per unit of standard deviation; overall risk

outperformance per unit of ß; systematic

Question 2

FundAlpha vs Fund Beta

Beta is an important risk measure, as it measures the …

Alpha (=Jensen’s alpha) measures the …

Some more things I did not understand-> review slide

Answer 2

sensitivity of the fund’s performance with respect to the benchmark index.

risk-adjusted outperformance of a fund.

Question 3

Outperformance vs Tracking error

Outperformance measures the … over a specified period of time.

• The tracking error (TE) is the …

If returns are measured on a daily basis, then under
the assumption of iid-returns it follows: (write the equation-> slide 7)

In order to account for systematic deviations from the benchmark, it is better to measure the TE as the standard deviation of the residuals of the following
equation: (write the equation-> slide 7)

The tracking error measures the risk of the deviation of the the fund’s return from
the benchmark return. It is typically high for actively managed funds (>6% p.a.) and low for passively managed funds (<4% p.a.)

Answer 3

return difference against the benchmark index

standard deviation of this outperformance measured on a yearly basis.

Check slide 7 for equations.

Question 4

Active versus Passive investing: How can a fund be identified?

Tracking Error of an active fund should be consistently higher than those of a passive fund.

An alternative measure: the Active Share equation. An active fund should have an active share of 50%.

Answer 4

AS = 0.5 summation | weight of stock i in fund - weight of stock i in benchmark |.

Question 5

Issues with alternative investment funds.

• Depending on their construction funds can be … (i.e. partnerships)
• Performance can be hard to track either because … (private equity) or because of discretion in …
• Management fees are significantly higher (∼2%) and come along with high performance fees (∼20%).
• … is very diverse, because of a wide range of different investment styles.

Answer 5

highly illiquid and/or difficult to access

underlying assets are not traded; reporting obligations

Risk profile

Question 6

Performance measurement when underlying assets are not traded (Private Equity Funds)

• For such funds performance is typically measured on the basis of … (cash flows).
• Either a so called money multiple (distributions/capital calls) or an … is calculated. As long as funds are not liquidated, the NAV is taken as a last cash flows.
• This approach suffers from several flaws: (i) …, (ii) how to aggregate returns over a family of funds?, (iii) how to calculate the risk underlying these funds?

Answer 6

observed capital calls and distributions

internal rate of return (IRR)

value weighted returns (IRRs) cannot be directly compared with time weighted returns

Question 7

Pitfalls in PE return measurements:

1. Do not compare returns on the basis of value-weighted returns (e.g. IRRs, mPMEs). WHY?
2. Pooled IRRs might be quite different from market returns even though time weighted returns are the same
3. Pooled IRRs might substantially outperform mPMEs, even though there is no risk- adjusted outperformance

Issue: How to disentangle risk-premia from genuine
outperformance (alpha) in PE?

Answer 7

Slides 33-35