PORTFOLIO THEORY AND THE CAPITAL ASSET PRICING MODEL

Question 1

EFFICIENT FRONTIER

Answer 1

Efficient portfolios provide the highest return for a given level of risk or least risk for given level of returns.

Curve that shows these points

Question 2

Assumptions of the Markowitz framework

Answer 2

• Investors prefer more consumption.
• Investors are rational.
• Investors are risk averse.
• Risk of a portfolio is based on the variability of its return.
• Model examines a single period of investor.

Question 3

Describe the relationship between risk and return on the efficient frontier diagram.

Answer 3

Top left - Low risk, high return
Top right - High risk, high return
Bottom left - Low risk, low return
Bottom right - High risk, low return

Question 4

RISK FREE ASSET

Answer 4

Standard deviation of zero.

When working out std dev only use wA^2*σ^A2

Question 5

Borrowing at the risk free rate.

Answer 5

Percentage borrowed at the risk free rate is negative. More than 100% invested in other firm.

Question 6

SHARPE RATIO

Answer 6

R-rf / σ

Question 7

MARKET PORTFOLIO

Answer 7

Portfolio with highest unit of reward per unit of risk.

Question 8

Assumptions of investors in the capital market theory

Answer 8

All investors capitalise on risk free asset opportunities and capital markets are perfectly competitive.

• Investors maximise utility functions that depend on the expected return and standard deviation of returns of portfolios.
• While individual utility functions vary all investors agree on the distribution of expected returns.

Question 9

Key assumptions of markets in the capital market theory

Answer 9

• There are no transaction costs or taxes to impede the operation of arbitrage processes.
• Information is cost less and as a result all investors are perfectly informed, and not surprisingly have identical expectations.

Question 10

SHARPE’S SINGLE INDEX MODEL

Answer 10

How do we account for different types of risk.
ri = E(ri) + mi + ei

Return is equal to the expected return, plus the impact of:

• Unanticipated systematic events, plus
• Unanticipated firm specific events

We can group all of the systematic risk events into one macroeconomic indicator and assume it moves the market as a whole.
All the remaining uncertainty is firm specific.

Question 11

MARKET RISK

Answer 11

How do we value market risk?

IRL: we cannot measure market risk directly, but we can see the effect it has on market returns (index returns).
-If market risk has a negative effect, then market returns fall
-If market risk has a positive effect, then market returns rise.
We can use this to IMPLY market risk

Question 12

Describe the security market line

Answer 12

Return on y axis, Beta on x axis.

Market portfolio is where beta = 1, the correlating return is the market return.

Risk free asset has a beta of zero and intercepts the y axis.

Question 13

SML equation

Answer 13

rf + β(rm - rf)

Question 14

CAPITAL ASSET PRICING MODEL

Answer 14

RELATIONSHIP BETWEEN PORTFOLIO AND MARKET RETURN

E(r)p = rf + βp * [E(rm) - rf]
Expected return on a security = risk free rate + beta of the security x difference between expected return on market and risk free rate

In a competitive market, the expected return on an investment is proportional to the level of risk undertaken.

Question 15

Using regression analysis to measure beta

Answer 15

• Obtain the historical time series of return (ri) on the stock of interest i.
• Obtain the historical time series of rf asset (e.g. t-bills).
• Take the difference between the two, and you’ll end up with a historical time series of risk premium of stock i, which is (ri - rf).
• Obtain the historical time series of the market return rm.
• Take the difference between rm and rf, and you’ll end up with a historical time series of market risk premium, which (rm - rf).
• Regress (ri - rf) on (rm - rf) to get the beta.

Question 16

Assumptions of CAPM

Answer 16

• Investors like high expected return and low standard deviation.
• Common stock portfolios that offer the highest expected return for a given standard deviation are known as efficient portfolios.
• If investing or borrowing at the rf rate of interest, one single portfolio is better to invest in than others, the market portfolio (point at which efficient frontier meets the SML).
• If market is efficient (no investor hold superior information) each investor would hold the market portfolio.
• CAPM applies to individual securities, as well as portfolios.

Question 17

What is the risk free rate in practice?

Answer 17

Annualised return on short term (1-3 month) or medium (10 year) government bonds.

Question 18

What is used for the expected return on market portfolio in practice?

Answer 18

Typically a broad market index, such as FTSE - All Share Index, S&P 500

Question 19

What if a stock doesn’t lie on the SML?

Answer 19

Above line - stock is under-priced

Below line - over-priced

Question 20

Diversifiable/undiversifiable risk on the SML

Answer 20

Slope of SML is non-diversifiable risk.

Difference between point on graph and SML is diversifiable risk.

Question 21

What are the problems when using CAPM?

Answer 21

Estimation of market risk premium:

1. Economic interpretation
   - What should the risk premium be?
   - What is the market portfolio?
2. Statistical uncertainty
   - Measurement using historical data subject to wide confidence interval.

Time variation in market risk premium

• Application of CAPM assumes risk premium constant over time.
• Not the case it practice.

Implies different rs for each time period being discounted.

Difficulty in estimating β:

• varies over time
• measurement error in estimation
• β determined in part by financial and operating leverage of company.

“Multifactor” models outperform “single factor” CAPM in practice
- Better job of explaining share price returns across companies.

Factors beyond sensitivity of stock to market (β).

Question 22

How can the uncertainty of β be reduced?

Answer 22

• Looking to industry average benchmarks.

- Adjusting beta for financial leverage effects.

Question 23

CONSUMPTION CAPITAL ASSET PRICING MODEL (CCAPM)

Answer 23

E(ri) = rf + βc(rm-rf)

where βc = Cov (r, consumption growth)/ Cov (rm, consumption growth)

Question 24

ARBITRAGE PRICING THEORY

Answer 24

Return = a + b (rfactor1) + b2 (rfactor2) + b3(rfactor3) + … + noise

Expected risk premium = r - rf
= b1(rfactor1 - rf) + b2 (rfactor2 - rf) + …

Question 25

THREE FACTOR MODEL

Answer 25

Used to calculate expected returns is the same as applying APT:

• Identify macroeconomic factors that could affect stock returns.
• Estimate expected risk premium on each factor (rfactor1 - rf, etc)
• Measure sensitivity of each stock to factors (b1, b2, etc)

r - rf = bmarket (rmarketfactor) + bsize (rsizefactor) + bBM (rBM)