PORTFOLIO THEORY AND THE CAPITAL ASSET PRICING MODEL Flashcards
EFFICIENT FRONTIER
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
Assumptions of the Markowitz framework
- 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.
Describe the relationship between risk and return on the efficient frontier diagram.
Top left - Low risk, high return
Top right - High risk, high return
Bottom left - Low risk, low return
Bottom right - High risk, low return
RISK FREE ASSET
Standard deviation of zero.
When working out std dev only use wA^2*σ^A2
Borrowing at the risk free rate.
Percentage borrowed at the risk free rate is negative. More than 100% invested in other firm.
SHARPE RATIO
R-rf / σ
MARKET PORTFOLIO
Portfolio with highest unit of reward per unit of risk.
Assumptions of investors in the capital market theory
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.
Key assumptions of markets in the capital market theory
- 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.
SHARPE’S SINGLE INDEX MODEL
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.
MARKET RISK
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
Describe the security market line
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.
SML equation
rf + β(rm - rf)
CAPITAL ASSET PRICING MODEL
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.
Using regression analysis to measure beta
- 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.
Assumptions of CAPM
- 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.
What is the risk free rate in practice?
Annualised return on short term (1-3 month) or medium (10 year) government bonds.
What is used for the expected return on market portfolio in practice?
Typically a broad market index, such as FTSE - All Share Index, S&P 500
What if a stock doesn’t lie on the SML?
Above line - stock is under-priced
Below line - over-priced
Diversifiable/undiversifiable risk on the SML
Slope of SML is non-diversifiable risk.
Difference between point on graph and SML is diversifiable risk.
What are the problems when using CAPM?
Estimation of market risk premium:
- Economic interpretation
- What should the risk premium be?
- What is the market portfolio? - 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).
How can the uncertainty of β be reduced?
- Looking to industry average benchmarks.
- Adjusting beta for financial leverage effects.
CONSUMPTION CAPITAL ASSET PRICING MODEL (CCAPM)
E(ri) = rf + βc(rm-rf)
where βc = Cov (r, consumption growth)/ Cov (rm, consumption growth)
ARBITRAGE PRICING THEORY
Return = a + b (rfactor1) + b2 (rfactor2) + b3(rfactor3) + … + noise
Expected risk premium = r - rf
= b1(rfactor1 - rf) + b2 (rfactor2 - rf) + …
THREE FACTOR MODEL
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)
