1. CAPM & SML I: Diversification Principle
Lecture 11
CAPM & SML I:
Diversification Principle

2. Topics covered in this lecture
Unsystematic risk, systematic risk and total risk
Measurement of systematic risk and total risk
Diversification principle
Portfolio Risk
Numerical Example
Practice Question

3. Unsystematic risk Diversifiable Risk Unique Risk Asset-specific Risk

4. Non-diversifiable Risk
Systematic Risk
Systematic Risk
Market Risk
Non-diversifiable Risk

5. Total Risk Total Risk Systematic Risk Unsystematic Risk
(Beta)
Total Risk
(Standard Deviation)

6. Risk Comparison Example
Stock A
Standard Deviation = 20%
Beta = 1.5
Stock B
Standard deviation = 12%
Beta = 2

7. Diversification Principle
Portfolio Risk
= Stock 1 Systematic Risk
+ Stock 2 Systematic Risk
+ Stock 3 Systematic Risk
Stock 1 Total Risk
Stock 2 Total Risk
Stock 3 Total Risk

8. Portfolio Risk
p = w11 + w22 + w33 + … + wNN

9. Numerical Example
We have a portfolio that invests equally in 3 mutual funds: Aggressive, Fundamentals, and Passive. The expected returns and betas on these funds are given below. Calculate the portfolio beta.
Aggressive Fund (A)
Fundamentals
(F)
Passive
(P)
Expected Return
30%
15% 5%
Beta
2.5
1.2
0.7

10. Numerical Example wA = wB = wC = 1/3
Portfolio Risk
= p
= wAA + wBB + wCC

11. A long time ago in a galaxy far far away … There was practice
You have a portfolio made up of a market index and an equity index. The portfolio beta is 1.6, and the beta on the market index is 1. If you are 40% invested in the market index, what is the beta on the equity index? p = 1.6 1 = 1 w1 = 0.4

12. Check Answers
w2 = 1 – 0.4 = 0.6 p = w11 + w22 1.6 = 0.4(1) + 0.62 1.6 – 0.4 = 0.62 2 = 1.2 / 0.6 = 2

13. End of Lecture 11 on Diversification Principle