Words of Caution when using Performance Evaluation
Performance evaluation is an historical exercise while most investors are interested in the future performance of portfolios.
Correcting the performance for risk is very difficult.
It is very difficult to obtain reliable estimates of the risk and return characteristics of individual securities.
The portfolio compositions change over time.
Are Mutual Funds Markowitz Efficient Investments?
The mutual funds are all inefficient investments
Funds tend to group into clusters corresponding to their investment goals
Mutual funds are required to publish written goal statements
In a few cases fund’s stated objective and performance differed
This income and growth fund performed in the same league as the growth funds .
Scrutinizing Mutual Funds Goal Statements Portfolio’s SDs and Betas were better indicators of portfolio’s actual performance than their goal statements. There are some funds which claim they are growth funds, but get lower return than income funds. # of funds claiming each goal Category’s average rate of return Beta Growth Growth & income Income & Growth Income, Growth & Stability Growth Growth & income Income & Growth Income, Growth & Stability 0.5 to 0.7 3 5 4 16 6.9% 10.1% 9.7% 9.1% 0.7 to 0.9 15 24 7 7 11.2% 10.0% 10.0% 12.2% 0.9 to 1.1 20 1 None 1 13.8% 9.5% None 13.5% Risk Class Range of Betas # of funds Average Beta Average Variance Average Rate of Return Low 0.5 to 0.7 28 0.619 0.000877 9.1% Medium 0.7 to 0.9 53 0.786 0.001543 10.6% High 0.9 to 1.1 22 0.992 0.002304 13.5%
The Avon Fund earned an average return of 8% annually with a standard deviation of 16.6%, while the Blair Fund earned 13.00% annually with a standard deviation of 22.4%. During the same time period the average risk-free rate was 4%.
Which fund was the better performer?
Since SHARPE Blair > SHARPE Avon , Blair was the better performer on a risk-adjusted basis.
SHARPE Example 12/27/09 Avon RFR 13% 8% 22.4% 16.6% Standard Deviation of Returns Expected Return, E(r) Blair Slope is 0.4018 for REVAR Blair Slope is 0.241 for REVAR Avon
The Avon Fund earned an average return of 8% annually (Characteristic Line AVON : Intercept : -0.00125; Beta : 0.8125), while the Blair Fund earned 13.00% annually (Characteristic Line BLAIR : Intercept : 0.014; Beta : 1.156). During the same time period the average risk-free rate was 4%.
Which fund was the better performer?
Since TREYNOR Blair > TREYNOR Avon , Blair was the better performer on a risk-adjusted basis.
Jensen’s alpha cannot be used to rank performance of different assets unless it’s adjusted for the assets’ risks ( same alphas does not imply same performance, because the vertical distance to the SML might be the same, but one fund might have much higher risk )
The appraisal ratio divides Jensen’s alpha by the standard error of the estimate (SE (u) ) which then allows for rankings
Notice that the alpha = intercept of the original characteristic line (used to estimate our beta) is not the same as Jensen’s alpha and should not be used for investment performance evaluation
Mutual funds with the highest average rate of return might not have the highest rank because
A highly aggressive fund may earn higher returns than a less aggressive fund but the higher returns may not be sufficient to compensate for the extra risk taken
Analyzing Performance Statistics While the Yak Fund earned twice as much as the Zebra Fund it is four times as risky. Possible Investments Expected Return Standard Deviation Yak Fund 30% 20% Zebra Fund 15% 5% RFR 4% 0%
(see notes in SML, the risk free interest rate has zero variance)
Analyzing Performance Statistics The leveraged Zebra portfolio dominates the Yak Fund; thus Zebra is a better fund even though Yak has a higher average return. Perhaps both Treynor and Jensen would give the same ranking in this case Yak RFR 48% 30% 20% 5% Standard Deviation Expected Return, E(r) Zebra Zebra’s SHARPE = 2.2 Yak’s SHARPE = 1.3 15% Yak’s AAL Zebra’s AAL
General Discussion of Performance Measurement Tools
When investors analyze merits of alternative investments, usually concerned with
Portfolio manager’s ability to select good investments and to not select poor investments
Sharpe, Treynor & Jensen’s Alpha are good tools to evaluate this issue
Portfolio manager’s ability to buy low/sell high and manager’s ability to react to changes in market’s direction
Sharpe, Treynor & Jensen’s Alpha are not good tools for evaluating market timing unless theoretical framework is extended