1. Capital Asset Pricing Model (CAPM)
Lecture 13
Capital Asset Pricing Model
(CAPM)

2. Topics covered in this lecture
The CAPM formula
Model interpretation
Model applications with numerical examples
Estimation of beta with market model
Practice question

3. CAPM formula E(Ri) = Rf + βi[E(RM) – Rf]
E(Ri) = expected return on an asset i
Rf = risk-free rate
βi = beta of asset I; a measure of systematic risk
E(RM) = expected return on the market portfolio that contains all assets
E(RM) – Rf
= Market risk premium, a measure of the excess return of the market portfolio over the risk-free rate

4. Determinants of expected return
CAPM => expected return on any asset depends on 3 factors:
Rf = Pure time value of money.
E(RM) – Rf = Reward for bearing risk.
βi = Level of systematic risk on asset i.
E(Ri) = Rf + βi[E(RM) – Rf]

5. CAPM applications
CAPM is used to obtain expected return on any asset or portfolio, as long as we are able to obtain the 3 factors:
Risk-free rate, Rf
Expected return on market portfolio, RM
Beta of the asset or portfolio, βi

6. Numerical Example 1: CAPM, 1 asset
Given the following information, calculate the expected return on the asset. Market data: T-Bill rate = 5% S&P 500 return = 15% Asset-specific data: Beta = 2

7. Numerical Example 2: CAPM, 1 portfolio, multiple assets
Given the following information, calculate the expected return on the portfolio. Market data: T-Bill rate = 5% S&P 500 return = 15% Portfolio-specific data: 5 stocks in portfolio: A, B, C, D, E Beta on assets: Investments in assets: βA = 0.5 A: $100,000 βB = 0.95 B: $200,000 βC = 1.52 C: $400,000 βD = 2.1 D: $200,000 βE = 2.32 E: $100,000

8. Numerical Example 2 (cont.)
Step 1: Find portfolio weights based on the market values of the investments. Portfolio weight on Asset i = $ Investment in i / Total portfolio value Note that the portfolio weights must sum up to 1.

9. Numerical Example 2 (cont.)
Step 2: Calculate portfolio beta. Portfolio beta = Sum of betas of assets in portfolio, weighted by their individuals portfolio weights.

10. Numerical Example 2 (cont.)
Step 3: Calculate the expected return on the portfolio using CAPM.
Rf = 0.05
RM = 0.15
Portfolio beta = 1.5
CAMP
E(RP) = Rf + βi[E(RM) – Rf]

11. Beta estimation
How did we get the asset betas in our previous example?
Market model:
Ri = a + bRM

12. Data required for market model
Company data:
- e.g., TELUS monthly stock prices
finance.yahoo.com
10 years (December 2000 – December 2010)
Market data:
e.g., S&P500 monthly index value
Calculate
Ri,t = (Pt – Pt-1) / Pt-1
RM,t = (It – It-1) / It-1

13. Month Ri Rm
Jan-01
Feb-01
Mar-01
Apr-01
May-01
Jun-01
Jul-01
Aug-01
Sep-01
Oct-01
Nov-01
Dec-01
Jan-10
Feb-10
Mar-10
Apr-10
May-10
Jun-10
Jul-10
Aug-10
Sep-10
Oct-10
Nov-10
Dec-10
0.0653

14. Market Model - Telus
Regressing Return on Telus against Return on S&P 500 (market index), we get RTelus = RM => Beta on Telus = βTelus = 1.11

15. Using estimated beta
Average return on S&P 500 = E(RM) = 0.11 Average return on 1-month US T-bill = Rf = 0.08 Using CAPM, βTelus = 1.11 E(RTelus) = Rf + βTelus (E(RM) – Rf)

16. Practice is more fun than skimming textbook!
Given the following information, calculate the expected return on the portfolio. S&P 500 expected return = 13% 3-month T-bill rate = 6% 3 assets in the portfolio: Solution on next slide.
Asset
Dollar invested
Beta X
$5,000
1.1 Y
$6,000
2.1 Z
$7,000
2.6

17. Solution to practice question
Step 1: Calculate portfolio weights. Total portfolio value = $ $ $7000 = $18000 Weight on X = wx = 5/18 Weight on Y = wy = 6/18 Weight on Z = wz = 7/18 Step 2: Calculate portfolio beta. βP = (5/18)(1.1) + (6/18)(2.1) + (7/18)(2.6) = Step 3: Calculate expected portfolio return. E(RP) = Rf + βP(E(RM) – Rf) = ( )(0.13 – 0.06) = = 20.12% (approximately)

18. End of Lecture 13 On
CAPM