# 10_Oheads - Lecture Notes 10 The Capital Asset Pricing...

This preview shows pages 1–6. Sign up to view the full content.

1 Lecture Notes 10 The Capital Asset Pricing Model Expected return, variance and standard deviation • The expected return on a security may be based: i. on the historical returns earned in the past, or ii. a fundamental analysis implying deviations from past returns. • We now want to contrast these two approaches. 1. Historical data • As we saw in the previous chapter, historical data on prices and dividends can be used to calculate: i. the percentage returns over T years R 1 , R 2 , R 3 , …, R T ; ii. the sample average percentage return R (1) iii. sample variance ( σ 2 ), and standard deviation ( σ ), of returns . (2) R R 1 R 2 R T +++ T -------------------------------------------- 1 T --- R t t 1 = T = σ 2 1 T 1 ------------ R t R () 2 t 1 = T =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 2. Fundamental analysis • In a fundamental analysis, we try to explain the key economic forces leading to stock price movements. • We build up a model of the underlying determinants of returns and use the model to forecast returns. • For example, as we noted at the beginning of the course, the business cycle is an important determinant of stock returns. • In particular, recessions correspond to the major periods of loss- es and booms the major periods of above-average gains. • We also examine economic factors affecting particular indus- tries (demand or cost shocks, new technologies or products), and then firms within each industry sector. • The fundamental approach is needed when the economic envi- ronment changes. Historical returns may then be of little use for forecasting future returns.
3 A simple model based on fundamental analysis • We might postulate a number of possible “states”, or situations: i. four “business cycle states” ( depression,” “recession,” “nor- mal” and “boom”); ii. three “industry demand” states; iii. two “firm demand share states”; and iv. three “firm cost states”. In total, there would be 4 × 3 × 2 × 3=72 possible “states of the world.” • Let π s be the joint probability of state s = 1,…,72 and R s the like- ly return in state s . The expected return on the stock would be (3) The expected variance ( σ 2 ) (and standard deviation σ ) would be (4) Numerical example . Suppose we have a model that predicts the ER π s R s s 1 = 72 = E σ 2 π s R s () 2 s 1 = 72 =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 following returns on two stocks A and B in three states: • Expected returns: μ A = (0.25)(0.20) + (0.50)(0.10) + (0.25)(0.00) = 0.l0 μ B = (0.25)(0.05) + (0.50)(0.10) + (0.25)(0.15) = 0.l0 Variances: Standard deviations: σ A = 0.005 = 0.07071, σ B = 0.00125 = 0.03536. Covariance and correlation • Covariance measures how two random variables are related. Table 1: Data for a fundamental analysis Outcome s Probability π s R A R B Boom 0.25 20% 5% Normal 0.50 10% 10% Recession 0.25 0% 15% σ A 2 0.25 () 0.20 0.1 2 0.5 0.1 0.1 2 0.25 0.0 0.1 2 ++ 0.005 = = σ B 2 0.25 0.05 0.1 2 0.5 0.1 0.1 2 0.25 0.15 0.1 2 0.00125 = =
5 • From two historical samples of T returns on stocks A and B : i. calculate the sample mean returns (5) ii. calculate the sample covariance using (6) If when R B > R B , R A > R A , and vice versa, returns on A and B will have a positive covariance .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 30

10_Oheads - Lecture Notes 10 The Capital Asset Pricing...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online