EC7092 Investment Management Active Portfolio ManagementActive portfolio management seeks to exploit perceived market ine ciencies. Two forms of active portfolio management market

EC7092 Investment ManagementActive Portfolio Management

Suresh Mutuswami

November 27, 2011

Suresh Mutuswami EC7092 Investment Management Active Portfolio Management

Road Map and Readings

The Efficient Markets Hypothesis (EMH) and ’beating themarket’

Active portfolio management

Market timingSecurity selection

Security selection: Treynor & Black model

Readings

BKM: Section 24.4, Chapter 27Other readings (optional)

Treynor, J.J. and Black F. (1973), “How to use securityanalysis to improve portfolio selection,” Journal of Business,46, 66-86.Black, F. and Litterman, R. (1992), “Global portfoliooptimization,” Financial Analysts Journal, September-October1992.


The problem

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 perceivedmarket inefficiencies.

Two forms of active portfolio management

market timingsecurity selection


Market Inefficiency

Actively-managed portfolios

are not fully diversifiedmay include mispriced securities

Competition amongst active managers ensures that securitiestrade close to their fair values.

on a risk-adjusted basis, most portfolio managers will not beatpassive strategies.managers with exceptional skills and/or privileged informationcan beat passive strategies.

Some active managers must earn abnormal profits, asotherwise . . .

there would be no active portfolio managers.security prices would stray from fair values, inducing portfoliomanagers to adopt active strategies.


Beating the market portfolio . . .


Market timing

Two techniques for improving performance:

adjust the bond/stock mix of the portfolio in anticipation ofmarket 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 overallportfolio and therefore we can use beta to measure howsuccessful market timing has been.


Market timing: adjusting stock-bond mix

There is little evidence of market timing ability.


Direct comparison with market return

Evaluate market timing by comparing the return on theportfolio with the return on the market

No market timing

average beta of portfolio (fairly) constantportfolio 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 is higher than market return.


Evidence of market timing: Returns comparison


Market timing: Merton’s example

holding period 1 January 1927 - 31 December 1978, with thefollowing investment strategies:

invest $ 1000 in 30-day T-bills, rolled over every 30 days.invest $ 1000 in NYSE index, and re-invest dividends.invest $ 1000 in either 30-day T-bills or NYSE index, switchingfrom one to the other every 30 days on the basis of perfectforesight (certainty).

How do the three strategies compare as of December 1978?

All in safe asset $ 3600

All equity $ 67,500

Perfect foresight $ 5, 360, 000, 000


Market timing

Why does perfect market timing result in such huge gains?

compounding over a large number of yearsprivileged information

Monthly returns on NYSE index and switching portfolio(σTBill = 2.10%, σequities = 22.14%):


Security selection

Aims at identifying mispriced securities which offeropportunity to achieve returns higher than pre-specifiedbenchmarks (or the market portfolio).

Problems:

adjusting composition of portfolio in favor of mispricedsecurities moves away from being full diversified.incur costs of carrying specific (or diversifiable) risk.

Trade-off between

achieving abnormal returns, andreducing risk via diversification.


Treynor-Black model: Preamble

The Treynor-Black model is a model embedding the use ofsecurity analysis.

Analysts look at the market and investigate in depth only fewsecurities (the others are assumed to be fairly priced). Theyform active portfolios as follows:

Estimate for each security betas and residual risk.Given a certain equilibrium model (say the CAPM), identifythe magnitude of mispricing (alpha).They also estimate the impact of holding a less than fullydiversified portfolio looking at the variance of stock residuals(residual risk).Given the estimates of betas, alphas and residual risks theycompute the optimal weights of each security in the activeportfolio.


Treynor-Black model: assumptions

Assume:there is a single common source of risk.the market is nearly efficient (i.e. the CAPM/single indexmodel nearly holds).

Asset returns are assumed to be given by:

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 mispricedsecurities):

E (rA) = αi + rf + βA[E (rM)− rf ]

with variance:

σ2(rA) = β2Aσ2M + σ2(eA)


Treynor-Black model: intuition


Treynor-Black model: solution

The optimal active portfolio is a combination of the passivemarket portfolio and the active portfolio of mispricedsecurities.

How do we judge the success of the strategy? Themathematics of the efficient frontier reveals that

S2P = S2

M +

[αA

σ(eA)

]2= S2

M +N∑i=1

[αi

σ(ei )

]2Only 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 orinformation ratio (squared).


Example

Equity analyst in HK selects the following mispriced stocks:

βi E (ri ) σ(ei )

BOC HK 0.6 20% 60%

MTR Corp. 0.6 17% 50%

Espirit Holdgs 0.5 14% 45%

Cathay Pacific 0.2 8% 40%

Other information: E (rM) = 10%, σRM = 25%,RF = 4%.


Example (continued)

Step 1: calculate expected abnormal returns and informationratios:

αi = E (ri )− rf − βi (E (rM)− rf ).

αiαi

σ(ei )

BOC HK 12.41% 0.21

MTR Corp. 9.40% 0.19

Espirit Holdgs 7.00% 0.16

Cathay Pacific 2.80% 0.07

This implies a Sharpe ratio of the active portfolio of

SP =

√√√√S2M +

4∑i=1

[αi

σ(ei )

]2= 0.41


Example (continued)

Step 2: construct the active portfolio implied by the securityanalyst input list.

The weight of each asset in the active portfolio is given by

wi =αi/σ

2(ei )∑4i=1 αi/σ2(ei )

αi/σ2(ei )

∑4i=1 αi/σ

2(ei )

BOC HK 0.344 0.28

MTR Corp. 0.376 0.30

Espirit Holdgs 0.346 0.28

Cathay Pacific 0.175 0.14

Total 1.241 1.00


Example (continued)

The formed active portfolio has the following characteristics.

αA =4∑

i=1

wiαi = 0.086 or 8.6%

βA =4∑

i=1

wiβi = 0.516

σ(eA) =

√√√√ 4∑i=1

w2i σ

2(ei ) = 0.264 or 26.4%


Example (continued)

The expected return and standard deviation of the activeportfolio are equal to:

E (rA) = αA + rf + βA[E (rM)− rf ] = 0.16 or 16%

σA =√β2Aσ

2M + σ2(eA) = 0.29 or 29%

cov(rA, rM) = β2Aσ2M = 0.032

ρ(rA, rM) =cov(rA, rM)

σAσM= 0.44


Example (continued)

Step 3: determine composition of the overall risky portfolio(active portfolio + market portfolio)

w0 =αA/σ

2(eA)

RM/σ2M

=⇒ w∗ =w0

1 + (1− βA)w0

where w∗ denotes the share of the active portfolio within theoverall risky portfolio. The weight attached to the marketportfolio within the overall risky portfolio is given by 1− w∗.

In our example,

w0 =0.086/(0.264)2

(0.1− 0.04)/(0.252)= 1.29

w∗ =1.29

1 + (1− 0.519)1.29= 0.80


Example (continued)

wi w∗

BOC HK 0.28× 0.80 = 0.22

MTR Corp. 0.30× 0.80 = 0.24

Espirit Holdgs 0.28× 0.80 = 0.22

Cathay Pacific 0.14× 0.80 = 0.11

Active Portfolio 0.80

Market Portfolio 0.20

Note that the Sharpe ratio of the active portfolio is 0.41 whichexceeds that of the market portfolio (0.24).


Example (continued)


Treynor-Black model: summing up

Optimizing model for portfolio managers who use securityanalysis under the assumption that markets are nearlyefficient.

security analysis can assess in depth only a small number ofsecurities (securities not assessed are assumed to be fairlypriced).market index portfolio is the passive portfolio.perceived mispricing guides the composition of the activeportfolio.


Treynor-Black model: summing up

Analysts follow several steps to make up the portfolio andevaluate 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 returnfor each security (abnormal return).

3 The nonsystematic risk component of the mispriced stock isthe cost of not fully diversifying by specialising in underpricedsecurities.

4 Determine the optimal weight of each security in the activeportfolio.

5 determine the optimal risky portfolio, which is a combinationof passive and active portfolios.

6 Compare CAL w.r.t CML


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EC7092 Investment Management Active Portfolio ManagementActive portfolio management seeks to exploit perceived market ine ciencies. Two forms of active portfolio management market