Invest 30/42 = .714 in P and .286 in T-bills
The return on P* is (.714) (.35) + (.286) (.06) =
26.7%
The managed portfolio underperformed by
1.3%.
Which Measure is Appropriate?
Suppose that our fund consists of many subportfolios. Which one is a better value added?
Since the portfolio is diversified, non-systematic risk is negligible and the appropriate metric is Treynor’s,
measuring excess return to the systematic risk .
We can also create a portfolio 𝑄∗ with a beta equal to that of 𝑃 and see if alpha of 𝑄∗ is interesting.
If the portfolio is not diversified, then use the Sharpe ratio. If we seek an active portfolio to mix with an index (passive)
portfolio, pick the one with higher information ratio.
P Q Market
Beta 0.9 1.6 1
Excess return 0.11 0.19 0.1
FN415.11 40 Practice Questions
Let 𝑟𝑀 = 0.14 and 𝑟𝑓 = 0.06. Find Alpha, Information ratio (𝛼/𝜎 𝜀 ), Sharpe ratio ( 𝑟𝑃 − 𝑟𝑓 /𝜎𝑃), and Treynor ratio ( 𝑟𝑃 − 𝑟𝑓 /𝛽𝑃).
Which portfolio is reasonable for us if: 1. We intend to hold only this portfolio.
2. This portfolio will be mixed with a previously chosen index fund. 3. The portfolio will be one of many subportfolios under our
A Simple Way to Measure Timing and Selection Success Bad selection ability Good selection ability Bad selection ability Good timing ability Good selection ability Good timing ability Good selection ability Good timing ability M f r r M f r r M f r r M f r r 2 1 2 P f M f M f P r r r r r r
FN415.11 42
Regress fund returns on indexes representing a range of asset classes.
The regression coefficient on each index measures the fund’s implicit allocation.
R–square measures return variability due to style or asset allocation.
The remainder is due either to security selection or to market timing.
FN415.11 44 Style Analysis: Kalman Filter
The procedure starts from the broadest asset allocation choices and progressively focus on ever-finer details of portfolio choice.
For example, we decompose overall performance into three components:
– Allocation choices across broad asset classes. – Industry or sector choice within each market. – Security choice within each sector.
FN415.11 46
Set up a benchmark portfolio:
Select a benchmark index portfolio for each asset class, e.g. SET index for equity.
Choose target weights structure, e.g. 60/40 rules.
The benchmark portfolio is set to have fixed
weights in each asset class, and its rate of return is given by
𝑟𝐵 =
𝑖=1 𝑁
𝑤𝐵𝑖𝑟𝐵𝑖
Attributing Performance to Components
𝑁 =number of asset classes in universe .
𝑤𝐵𝑖 =the weight of the benchmark in asset class 𝑖.
Form a managed portfolio:
Choose weights 𝑤𝑃𝑖 based on market expectations.
Choose securities within each class by security analysis, which earns 𝑟𝑃𝑖 over the evaluation period.
The return of the managed portfolio will be
𝑟𝑃 =
𝑖=1 𝑁
𝑤𝑃𝑖𝑟𝑃𝑖
Attributing Performance to Components
𝑁 =number of asset classes in universe . 𝑤𝑃𝑖 = the weight of asset class 𝑖.
FN415.11 48 Explain the Difference in Return
1 1 1 1 1 ( ) n n B Bi Bi P Pi Pi i n n i n P B Pi Pi Bi Bi Pi Pi Bi Bi i i i Pi Pi Bi Bi Pi Bi Bi Pi Pi Bi r w r r w r r r w r w r w r w r w r w r w w r w r r
Contribution from asset allocation
Contribution from security selection Total contribution from asset class 𝑖
Explain the Difference in Return
Return of asset class
Weight of asset class
Pi w Bi w Bi r Pi r
Benchmark return from 𝑖th asset class = 𝑤𝐵𝑖𝑟𝐵𝑖 Added by selection Added by alloc at ion
Let the benchmark portfolio follows 60/40 rule.
FN415.11 50
FN415.11 52
Should we measure a fund manager’s investment performance over an entire market cycle?
Yes:
– A manager could be a better performer in one type of
circumstance than in another, e.g. high beta portfolio will do better in up markets and worse in down markets.
– More observations would improve the reliability of the measurement.
Not necessary:
– If one control for exposure to the market (i.e. adjust for beta), then market performance should not affect the relative
performance of individual managers meaning that it is not necessary to wait for an entire market cycle.
Extrapolating from historical data = driving by looking only at the rear-view mirror.
Risk manager is the real expert in the domain that is dominated by outliers, not a fortune teller.
When everybody starts to implement the similar
optimal strategy or possessed by herding behavior in extreme market condition
– London bridge: instinct tell us that the only way to keep a balance is to walk in sync with other people
https://www.youtube.com/watch?v=eAXVa__XWZ8
– Metronomes synchronization: when people are connected during a crisis
https://www.youtube.com/watch?v=W1TMZASCR-I