capital allocation, asset allocation and the efficient market hypothesis part a otto khatamov

Capital Allocation, Asset Allocation and the Efficient Market Hypothesis

Part A

Otto Khatamov

1. Client needs: Investment policy statement• Focus: Investor’s short-term and long-term needs,

expectations

2. Portfolio manager: Examine current and projected financial, economic, political, and social conditions• Focus: Short-term and intermediate-term expected conditions

to use in constructing a specific portfolio

3. Portfolio manager: Implement the plan by constructing the portfolio• Focus: Meet the investor’s needs at minimum risk levels

4. Client/Portfolio manager: Feedback loop• Monitor and update investor needs, environmental conditions,

evaluate portfolio performance

SeriesGeometric Average

Arithmetic average

Standard Deviation

Small-Company Stocks

11.64% 17.74% 39.30%

Large-Company Stocks

10.01% 12.04% 20.55%

Long-Term Government Bonds

5.38% 5.68% 8.24%

US Treasury Bills 3.78% 3.82% 3.18%Source: BKM Chapter 5 – Sources: Returns on T-bills, large and small stocks – CRSP, T-bonds - RSP for 1926-1995 returns and Lehman Brothers long-term and intermediate indexes for 1996 and later returns.

What are the sources of differences in risk, returns and risk premiums?

Types of risks: Business risk/Financial risk/Liquidity risk – i.e. BA

decides to buy 20 new planes. Industry risk – i.e. Subprime crisis Country risk/Exchange rate risk – i.e. Iceland Krona,

recession in the economy

Investors may held a portfolio of different assets

What happens to the risk of a portfolio as we add more assets?

Risk that can be eliminated by diversification is called unsystematic risk whereas risk that remains is called systematic risk.

The concept of diversification: An The concept of diversification: An example of Systematic vs example of Systematic vs Unsystematic risk Unsystematic risk

Debt Mutual FundEquity Mutual

Fund

Expected return, E(r)

8% 13%

Standard deviation, σ

12% 20%

Correlation, pD,E 1

1 If )(

2

138)()()(

,22

,22222

EDEEDD

EDEDEDEEDD

EDEEDDp

ww

wwww

wwREwREwRE

p

p

The concept of The concept of diversification:diversification:Systematic vs Unsystematic Systematic vs Unsystematic risk risk

Unsystematic risk

Systematic risk

No of Shares

Standard Deviation

Why not continue to add stocks / assets to our portfolios?

The Efficient set with the market portfolio and a risk-free asset

σ

Rp

Rf

M (Market Portfolio)E(Rm)

σΜ

“How to allocate the capital between the market and the risk free asset?”

… That decision has been shown to account for an astonishing 94% of the differences in total returns achieved by institutionally managed pension funds. There is no reason to believe that the same relationship does not also hold true for individual investors… (J. Bogle, Chairman of the Vanguard group of investment companies).

Capital Allocation between the risk free asset and the market portfolio

“How to allocate the capital between the market and the risk free asset?”

Feasible risk return combinations:• Let assume we have decided the proportion of investment

asset, w1 to be allocated in the market portfolio and w2 in the risk free.

What is the expected return and the variance of the portfolio?

221,21

222

221

2

21

2

)()(

mfmrfrmfm

fmp

wwwww

rwREwRE

p

Capital Allocation between the risk free asset and the market portfolio

σ

Rp

Rf

M

0 < w 1 < 1

w

1 > 1

E(Rm)

σm

Capital Allocation between the risk free asset and the market portfolio: The role of risk tolerance…

How to choose the complete portfolio from among the feasible risk return combinations? • Let assume y = w1, the portion of money to be allocated in

the market portfolio and 1-y = w2 the portion of money to be allocated in the risk free.

The purpose is to maximise our utility by choosing the best allocation to the risky asset, y.


2*

2*

22

y

222

y

01.0

])([

001.0])([

005.0])([

005.0)1()(005.0)(

m

fm

mfm

mfmf

mfmcc

A

rREy

AyrREy

U

AyrREyrUMAX

AyryRyEAREUMAX

222

)1()()(

mc

fmc

y

ryRyERE


Utility as a function of allocation to the market portfolio (y) …

Complete portfolio using an indifference curve …

Capital allocation line: In practice…

It is impossible to invest in the market portfolioo Limits to diversification benefits

• Transaction costs• Private information

o Some assets are not traded• Human capital

Invest in an optimal risky portfolioo How to create the optimal risky portfolio?

How to determine the assets to include in the risky portfolioo Efficient Market Hypothesis

• Passive strategy • Active strategy

Let assume we can invest in two risky funds, bonds and stocks and the risk free asset

Graphical representation of the feasible risk return combinations…

Debt Mutual Fund

Equity Mutual Fund

Risk Free Asset


8% 13% 5%


12% 20% 0

Correlation, pD,E 0.3

The mathematics of optimal risky portfolio using two risky assets

DE

22

2

D

D

DpDEpp

2

1i

pp

w

w1w

),cov(])()([])([])([

),cov(])([])([w

...for w solve and zero toequal derivative partial Set the

. wrespect to with S of derivative partial theTake .w-1 w theand the),E(r theSubstitute :Solution

1 s.t.

)E(rS Max

i

EDfEfDDfEEfD

EDfEfD

i

p

f

rrrrErrErrErrE

rrrrErrE

w

r

E

6.04.01w1w

4.072)51358(144)513(400)58(

72)513(400)58(w

),cov(])()([])([])([

),cov(])([])([w

DE

D

22

2

D

EDfEfDDfEEfD

EDfEfD

rrrrErrErrErrE

rrrrErrEE

Back to the example…

Debt Mutual Fund

Equity Mutual Fund

Risk Free Asset


8% 13% 5%


12% 20% 0

Correlation, pD,E 0.3

Markowitz portfolio selection problem: Generalized portfolio construction to the case of many risky securities and a risk free asset

Standard Deviation

Expected Returns

Risky Assets

Markowitz portfolio selection problem: Feasible risk-return combinations

0,...vb b)E(r (2) and 1w (1) s.t.

Min

OR

0,...z σ (2) and 1w (1) s.t.

)E(r Max

p

N

1ii

2p

wi

2p

N

1ii

pw i

Markowitz portfolio selection problem: Feasible risk-return combinations

Standard Deviation

Expected Returns

Risky Assets

Efficient Frontier

Minimum-variance Frontier

Minimum Variance

Markowitz portfolio selection problem: Find the optimal risky portfolio

1 s.t.

)E(rS Max

N

1i

pp

w i

i

p

f

w

r

Markowitz portfolio selection problem: Find the optimal risky portfolio

Standard Deviation

Expected Returns

Risky Assets

Efficient Frontier


Minimum Variance

Optimal risky portfolio

CAL

Markowitz portfolio selection problem: Find the complete portfolio

Standard Deviation

Expected Returns

Risky Assets

Efficient Frontier


Minimum Variance

Optimal risky portfolio

CAL

o Specify the characteristics of all securities• Expected returns, variances, correlations

o Asset allocation to find the optimal risky portfolio• Create the efficient frontier• Find the weights that maximise the Sharpe ratio (CAL)• Using these weights calculate the expected return and the variance of the optimal portfolio

o Capital allocation between the optimal risky portfolio and the risk free asset

• Maximise the Utility of the investor and find the y* (i.e. portion of money to be allocated in the optimal risky portfolio)• Calculate the portion of money to be allocated in the risk free portfolio and the expected return and the variance of the complete portfolio

Capital allocation line: In practice…

It is impossible to invest in the market portfolioo Limits to diversification benefits

• Transaction costs• Private information

o Some assets are not traded• Human capital

Invest in an optimal risky portfolioo How to allocate the proportion of assets to create

the optimal risky portfolio? How to determine the assets to include in

the risky portfolioo Efficient Market Hypothesis

o Passive strategy o Active strategy

Kendal (1953) identify no predictable patterns in stock prices – stock prices evolve randomly Irrational market (Market psychology) Rational market

Example…

Suppose that stock prices are predictable – XYZ stock price will rise in three days by 10%.

Action (Immediately reflect good news): ◦ If you do not hold XYZ stock – Buy XYZ◦ If you hold XYZ stock – Do not sell XYZ

A forecast about future performance leads to changes in current performance

Stock prices reflect all available stock information

Why are price changes random?◦ Prices react to information (If it could be

predicted, then the prediction would be part of today’s stock price)

◦ Thus, flow of new information (cannot be predicted) is random

◦ Therefore, price changes are random

Random price changes indicate a rational market…

Why should stock prices fully and accurately reflect all available information?◦ Information may be costly to uncover and

analyze thus need the appropriate reward

Intensive competition among market participants assures prices reflect all information

Forms of the EMH:◦ Weak (Prices will reflect all information that can be

derived from trading historical data such past prices and trading volume)

◦ Semi-strong (Prices will reflect all publicly available information regarding the prospects of the firm)

◦ Strong (Prices would reflect all information relevant to the firms’ prospects, even inside information)

Active or Passive Management?◦Passive Management (Proponents of EMH – stock

prices are at fair levels) Index Funds (well-diversified portfolios)

◦Active Management Security analysis (Technical and Fundamental

analysis) Timing

What would happen to market efficiency if all investors follow a passive strategy?

Active or Passive Management? The empirical evidence…

Source: Fund data provided by Morningstar; index data provided by Thomson Financial – The Active – Passive debate: Bear Market Performance, 2008, C Philips, Vanguard .

Active or Passive Management? The empirical evidence…◦Mutual fund risk adjusted performance

Malkiel, 1995, Returns from Investing in Mutual Funds 1971-1991, Journal of Finance

◦Superior analysts (SAT, MBA) Chevalier and Ellison, 1999, Are Some Mutual Fund Managers

Better than Others? Cross Sectional Patterns in Behavior and Performance, Journal of Finance

◦ Informed vs Uninformed investors Barber, Lie, Liu and Odean, 2008, Just how Much do Investors

Lose by Trading?, Review of Financial Studies

• Bodie, Kane and Marcus, Chapter 7-8-13

capital allocation, asset allocation and the efficient market hypothesis part a otto khatamov

Documents