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Homework answers / question archive / (b) Please outline and explain the rationale, advantages and disadvantages (if any) for the portfolio selection methodology proposed by Treynor and Black, under the assumption that the model of asset returns is the Single Index Model with the market factor as the sole index
(b) Please outline and explain the rationale, advantages and disadvantages (if any) for the portfolio selection methodology proposed by Treynor and Black, under the assumption that the model of asset returns is the Single Index Model with the market factor as the sole index. In your answer, at a minimum, you should i. 11. List and briefly describe the inputs required to implement the portfolio selection methodology proposed by Treynor and Black, under the assumption that the model of asset returns is the Single Index Model with the market factor as the sole index. Outline and offer an intuitive explanation of the rationale for the key steps that must be undertaken to form mean-variance optimal portfolios according to the methodology proposed by Treynor and Black, under the assumption that the model of asset returns is the Single Index Model with the market factor as the sole index. Explain the overall rationale of the above portfolio construction methodology, pointing out advantages and disadvantages, ideally relating it to modern approaches to portfolio choice such as so called "factor investing".
Treynor-Black Dual Portfolio
The passively invested market portfolio contains securities in proportion to their market value, such as with an index fund. The investor assumes that the expected return and standard deviation of these passive investments can be estimated through macroeconomic forecasting.
Is it possible to beat the performance of a passive portfolio?
− If markets are fully efficient, the answer is NO
− But… what if markets are only nearly efficient
Active portfolio management seeks to exploit perceived market inefficiencies
Two forms of active portfolio management
− market timing
− security selection
Market inefficiency
Actively-managed portfolios
− are not fully diversified
− may include mispriced securities
Competition amongst active managers ensures that securities trade close to their fair values
− on a risk-adjusted basis, most portfolio managers will not
beat passive strategies
− managers with exceptional skills and/or privileged information can beat passive strategies
Some active managers must earn abnormal profits
− otherwise …
° there would be no active portfolio managers
° security prices would stray from fair values, inducing portfolio managers to adopt active strategies
Market timing
Two techniques for improving performance:
− adjust the bond/stock mix of the portfolio in anticipation of market changes
° modify portfolio in favour of equities (bonds) if investor is “bullish” (“bearish”) about the stock market − adjust the equity beta of the portfolio
° invest in high-beta (low-beta) stocks if investor is “bullish” (“bearish”) about the stock market
Both techniques impact the average beta of the overall portfolio therefore we can use beta to measure how successful market timing has been Direct comparison with market return
Evaluate market timing by comparing the return on the portfolio with the return on the market
No market timing
− average beta of portfolio (fairly) constant
− portfolio return is a constant fraction of return on market (assuming no specific risk)
Market timing
− high β in rising market, low β in falling market
− portfolio return > market return
Security selection
Aims at identifying mispriced securities which offer opportunity to achieve returns higher than
pre-specified benchmarks (or the market portfolio)
Problems:
− adjusting composition of portfolio in favour of mispriced securities moves away from being full
diversified
− incur costs of carrying specific (or diversifiable) risk
Trade-off between
− achieving abnormal returns
− reducing risk via diversification
Treynor-Black model: preamble
The Treynor-Black model is a model embedding the use of security analysis
Analysts look at the market and investigate in depth only few securities (the others are assumed to be fairly priced). They form active portfolios as follows:
− Estimate for each security betas and residual risk
− Given a certain equilibrium model (say the CAPM) the identify
the magnitude of mispricing (alpha)
− They also estimate the impact of holding a less than fully diversified portfolio looking at the variance of stock residuals (=residual risk)
− Given the estimates of betas, alphas and residual risks they compute the optimal weights of each security in the active portfolio
Treynor-Black model: assumptions
− there is a single common source of risk
− the market is nearly efficient (i.e. the CAPM/single index model nearly holds)
Asset returns: Rk=Rf +βk(Rm-Rf)+Ek+ αk
where αk is the abnormal return (=Jensen’s alpha) of themispriced assets k.
Expected return on active portfolio (comprising mispriced securities)
:E(Ra)=α+Rf+βa(E(Rm)-Rf)
Treynor-Black model: solution
The optimal active portfolio is a combination of the passive market portfolio and the active portfolio of mispriced securities
How do we judge the success of the strategy? The mathematicsof the efficient frontier reveals that
Only for the optimal active portfolio (P), the Sharpe ratio (squared) is given by the sum of
− the sharpe ratio of the (passive) market portfolio (squared)
− the standardised degree of mispricing, appraisal ratio or information ratio, (squared)
Treynor-Black model: summing up
Optimizing model for portfolio managers who use security analysis under the assumption that markets are nearly efficient
− security analysis can assess in depth only a small number of securities (securities not assessed are assumed to be fairly priced)
− market index portfolio is the passive portfolio
− perceived mispricing guides the composition of the active portfolio
Treynor-Black model: summing up
− analysts follow several steps to make up the portfolio and evaluate its expected performance
1. Estimate beta and residual risk for each analysed security; from these, determine the required return
2. Given the degree of mispricing, determine the expected return for each security (abnormal return)
3. The non-systematic risk component of the mispriced stock is the cost of not fully diversifying by specialising in underpriced securities
4. Determine the optimal weight of each security in the active portfolio
5. determine the optimal risky portfolio, which is a combination of passive and active portfolios
6. Compare CAL w.r.t CML
Treynor-Black Dual Portfolio
The passively invested market portfolio contains securities in proportion to their market value, such as with an index fund. The investor assumes that the expected return and standard deviation of these passive investments can be estimated through macroeconomic forecasting.
In the active portfolio—which is a long/short fund, each security is weighted according to the ratio of its alpha to its unsystematic risk. Unsystematic risk is the industry-specific risk attached to an investment or an inherently unpredictable category of investments. Examples of such risk include a new market competitor who gobbles up market share or a natural disaster that destroys revenue.
The Treynor-Black ratio or appraisal ratio measures the value the security under scrutiny would add to the portfolio, on a risk-adjusted basis. The higher a security's alpha, the higher the weight assigned to it within the active portion of the portfolio. The more unsystematic risk the stock has, the less weighting it receives.
Final Thoughts on Treynor-Black
The Treynor-Black model does provide an efficient way of implementing an active investment strategy. Because it is hard to pick stocks accurately as the model requires, and restrictions on short selling may limit the ability to exploit market efficiencies and generate alpha, the model has gained little traction with investment managers.
Is it possible to beat the performance of a passive portfolio?
− If markets are fully efficient, the answer is NO
− But… what if markets are only nearly efficient
Active portfolio management seeks to exploit perceived market inefficiencies
Two forms of active portfolio management
− market timing
− security selection
Market inefficiency
Actively-managed portfolios
− are not fully diversified
− may include mispriced securities
Competition amongst active managers ensures that securities trade close to their fair values
− on a risk-adjusted basis, most portfolio managers will not
beat passive strategies
− managers with exceptional skills and/or privileged information can beat passive strategies
Some active managers must earn abnormal profits
− otherwise …
° there would be no active portfolio managers
° security prices would stray from fair values, inducing portfolio managers to adopt active strategies
Market timing
Two techniques for improving performance:
− adjust the bond/stock mix of the portfolio in anticipation of market changes
° modify portfolio in favour of equities (bonds) if investor is “bullish” (“bearish”) about the stock market − adjust the equity beta of the portfolio
° invest in high-beta (low-beta) stocks if investor is “bullish” (“bearish”) about the stock market
Both techniques impact the average beta of the overall portfolio therefore we can use beta to measure how successful market timing has been Direct comparison with market return
Evaluate market timing by comparing the return on the portfolio with the return on the market
No market timing
− average beta of portfolio (fairly) constant
− portfolio return is a constant fraction of return on market (assuming no specific risk)
Market timing
− high β in rising market, low β in falling market
− portfolio return > market return
Security selection
Aims at identifying mispriced securities which offer opportunity to achieve returns higher than
pre-specified benchmarks (or the market portfolio)
Problems:
− adjusting composition of portfolio in favour of mispriced securities moves away from being full
diversified
− incur costs of carrying specific (or diversifiable) risk
Trade-off between
− achieving abnormal returns
− reducing risk via diversification
Treynor-Black model: preamble
The Treynor-Black model is a model embedding the use of security analysis
Analysts look at the market and investigate in depth only few securities (the others are assumed to be fairly priced). They form active portfolios as follows:
− Estimate for each security betas and residual risk
− Given a certain equilibrium model (say the CAPM) the identify
the magnitude of mispricing (alpha)
− They also estimate the impact of holding a less than fully diversified portfolio looking at the variance of stock residuals (=residual risk)
− Given the estimates of betas, alphas and residual risks they compute the optimal weights of each security in the active portfolio
Treynor-Black model: assumptions
− there is a single common source of risk
− the market is nearly efficient (i.e. the CAPM/single index model nearly holds)
Asset returns: Rk=Rf +βk(Rm-Rf)+Ek+ αk
where αk is the abnormal return (=Jensen’s alpha) of themispriced assets k.
Expected return on active portfolio (comprising mispriced securities)
:E(Ra)=α+Rf+βa(E(Rm)-Rf)
Treynor-Black model: solution
The optimal active portfolio is a combination of the passive market portfolio and the active portfolio of mispriced securities
How do we judge the success of the strategy? The mathematicsof the efficient frontier reveals that
Only for the optimal active portfolio (P), the Sharpe ratio (squared) is given by the sum of
− the sharpe ratio of the (passive) market portfolio (squared)
− the standardised degree of mispricing, appraisal ratio or information ratio, (squared)
Treynor-Black model: summing up
Optimizing model for portfolio managers who use security analysis under the assumption that markets are nearly efficient
− security analysis can assess in depth only a small number of securities (securities not assessed are assumed to be fairly priced)
− market index portfolio is the passive portfolio
− perceived mispricing guides the composition of the active portfolio
Treynor-Black model: summing up
− analysts follow several steps to make up the portfolio and evaluate its expected performance
1. Estimate beta and residual risk for each analysed security; from these, determine the required return
2. Given the degree of mispricing, determine the expected return for each security (abnormal return)
3. The non-systematic risk component of the mispriced stock is the cost of not fully diversifying by specialising in underpriced securities
4. Determine the optimal weight of each security in the active portfolio
5. determine the optimal risky portfolio, which is a combination of passive and active portfolios
6. Compare CAL w.r.t CML
In the active portfolio—which is a long/short fund, each security is weighted according to the ratio of its alpha to its unsystematic risk. Unsystematic risk is the industry-specific risk attached to an investment or an inherently unpredictable category of investments. Examples of such risk include a new market competitor who gobbles up market share or a natural disaster that destroys revenue.
The Treynor-Black ratio or appraisal ratio measures the value the security under scrutiny would add to the portfolio, on a risk-adjusted basis. The higher a security's alpha, the higher the weight assigned to it within the active portion of the portfolio. The more unsystematic risk the stock has, the less weighting it receives.
Final Thoughts on Treynor-Black
The Treynor-Black model does provide an efficient way of implementing an active investment strategy. Because it is hard to pick stocks accurately as the model requires, and restrictions on short selling may limit the ability to exploit market efficiencies and generate alpha, the model has gained little traction with investment managers.
