Week 8 - Active portfolio management & performance evaluation Flashcards
What is Market timing?
*extreme foresight strategy
- Managers have market timing ability if they can FORECAST when to be IN the EQUITY MARKET and when to be OUT of the market (hold cash or risk-free asset).
- This implies NON-LINEAR RELATIONSHIP between excess portfolio returns and excess market return: the excess portfolio return is MORE SENSITIVE to the market in GOOD TIMES.
- Funds that have market timing ability invest more in the market during good times and less in bad times.
- Hence, their portfolios have HIGHER BETAS w.r.t. the MARKET when the market is doing well.
- Their portfolio has a high β when they expect the return on the market to exceed the risk-free rate.
– Their portfolio has a low β when they expect the return on the market to be dominated by the risk-free rate.
- CONVEX
(non-linearity cannot be explained well by Sharpe ratios; use non-linear regression and non-linear factors instead)
- The regression coefficients for the non-linear terms have to be positive and significant
Treynor-Black model - intuition and logic
- Select a SMALL SET of securities you think are MISPRICED (ie. have +ve or -ve alphas)
- This active portfolio A is likely to be under-diversified
- Combine this active portfolio with the MARKET (passive benchmark portfolio M) to diversify
» rp = w rA + (1-w) rM - Calculate a capital allocation line (CAL)
- Use your utility function to determine your optimal portfolio
- find optimal weight that maximises the Sharpe ratio
*then linked to Sharpe ratio^2 and Appraisal ratio of portfolio A
» by mixing with the market, we achieve a HIGHER Sharpe ratio at point T, as well as reducing idiosyncratic risk
Performance measure - Sharpe ratio + when to use
- captures the RISK-RETURN TRADEOFF
- If SRp > SRM then P has outperformed the market; otherwise, P has underperformed the market.
- uses TOTAL RISK, so better when we are looking at whole portfolios, rather than individual assets
» (limitation: takes into account only MEAN and STD DEV; not useful when investors care about skewness and Kurtosis)
» nonetheless, Sharpe ratio is the easiest and most popular performance measure
- Use when the portfolio represents the entire investment fund
Performance measure - M-squared
What are the advantages of this measure relative to the Sharpe ratio?
[2018]
- FIXES RISK (denominator = variance of market) and only considers DIFFERENCE IN RETURN → more meaningful comparisons between portfolios b/c same volatility
1. Numerical value of the Sharpe ratio is difficult to interpret, whether it is big or small.
2. mix portfolio P with T-bills so that std dev of the resulting portfolio P* is the same as the market portfolio M - P* is better than M if it has higher expected return
» M^2 is a transformation of the Sharpe ratio and has the same ranking as the Sharpe ratio
eg. if A has a higher Sharpe ratio than B, A also has higher M^2 than B
Performance measure - Jensen’s alpha + significance
- the usual alpha w.r.t. CAPM
- The MAXIMUM amount you should be WILLING TO PAY a manager
- if you are using past alpha, this assumes that the manager’s future performance will be the same as their past performance
Performance measure - Treynor measure (Treynor’s ratio) + when to use
= the SLOPE of the line connecting the ASSET to the RISK-FREE // the slope of the SML for the actively managed portfolio
- any asset that obeys CAPM, ie. lies on SML, has a Treynor measure = market risk premium
- if Treynor measure > MRP which means larger slope, positive alpha
- if Treynor measure < MRP which means smaller slope, negative alpha
- Use for investments that form a small portfolio of a portfolio // when portfolio P is one actively managed portfolio out of many that you are adding to a passive portfolio
*formula is similar to the Sharpe ratio, except that the denominator is BETA rather than sigma
Performance measure - Appraisal ratio + when to use
= alpha per unit of IDIOSYNCRATIC RISK
- the problem with Jensen’s alpha is that it does not adjust for idiosyncratic risk in the portfolio
- AR guides how much of an asset/fund to add to portfolio
- Use when an actively managed portfolio is optimally mixed with the passive portfolio
Treynor vs Jensen
- Treynor’s measure and alpha always agree in their under/outperformance judgments relative to the market M
- However, they may not rank portfolios in the same fashion
- Ratio alpha/beta is abnormal return per unit of systematic risk (see formula on slide)
Sharpe ratio vs Treynor’s ratio
Sharpe ratio
1. uses TOTAL RISK
2. appropriate for ENTIRE INVESTMENT PORTFOLIO
Treynor’s ratio
1. uses BETA (covariance with the market)
2. useful for investments that form a SMALL PART of a PORTFOLIO
- both measures the risk vs. excess return tradeoff, but have diff. definitions of risk
- both are useful for RANKING investment opportunities
2 regression equations to test managers’ Market timing ability
(see notes for formulas)
*must know how to DRAW GRAPH
- Henriksson and Merton
- INDICATOR FUNCTION, I_t of the return on the market - risk free
- if rMt - rft > 0, indicator function = 1
- otherwise, indicator function = 0
- if gamma_p > 0 and significant, then there is evidence of timing ability
- Henriksson finds that 62% of funds have negative timing ability - Treynor and Mazuy
- focus on (r_Mt - r_ft)^2
- if gamma_p > 0, then there is timing ability
- the value of stock selection is the alpha from this regression
- Treynor and Mazuy find no evidence of market timing ability
