Ross7eCh11

• The ith stock in the list have returns:
Ri = Ri + βi F + εi
Relationship Between the Return on the Common Factor & Excess Return
bi =
Cov ( Ri , RM )
2 ( RM )
• We shall now consider many types of systematic risk.
11.3 Systematic Risk and Betas
• For example, suppose we have identified three systematic risks on which we want to focus:
11.1 Factor Models: Announcements, Surprises, and Expected Returns
• The return on any security consists of two parts.
– First the expected returns – Second is the unexpected or risky returns.
11.8
Summary and Conclusions
Arbitrage Pricing Theory
Arbitrage arises if an investor can construct a zero investment portfolio with a sure profit.
• Since no investment is required, an investor can create large positions to secure large levels of profit. • In efficient markets, profitable arbitrage opportunities will quickly disappear.
Systematic Risk and Betas
11.4
11.5
Portfolios and Factor Models
Betas and Expected Returns
11.6 The Capital Asset Pricing Model and the Arbitrage Pricing Theory 11.7 Parametric Approaches to Asset Pricing
3.
The dollar-euro spot exchange rate, S($,€)
•
Our model is:
Systematic Risk and Betas: Example
R = R + βI FI + βGDP FGDP + βS FS + ε Suppose we have made the following estimates:
1. 2. Inflation GDP growth
R = R +m +ε R = R + βI FI + βGDP FGDP + βS FS + ε βI is the inflation beta βGDP is the GDP beta βS is the spot exchange rate beta ε is the unsystematic risk
Finally, if it was the case that the expected return on the stock was 8%, then
R = 8%
R = 8% - 2.30 5% + 1.50 (-3%) + 0.50 (-10%) + 1% R = -12%
11.4 Portfolios and Factor Models
• A way to write the return on a stock in the coming month is:
R = R +U where
R is the expected part of the return
U is the unexpected part of the return
11.1 Factor Models: Announcements, Surprises, and Expected Returns
• Any announcement can be broken down into two parts, the anticipated or expected part and the surprise or innovation: • Announcement = Expected part + Surprise.
11.2 Risk: Systematic and Unsystematic
We can break down the risk, U, of holding a stock into two components: systematic risk and unsystematic risk: Total risk; U
• The expected part of any announcement is part of the information the market uses to form the expectation, R of the return on the stock.
• The surprise is the news that influences the unanticipated return on the stock, U.
= actual – expected
= 8% – 3% = 5%
R = R - 2.30 ´ 5% +1.50 ´ FGDP + 0.50 ´ FS +1%
Systematic Risk and Betas: Example
R = R - 2.30 ´ 5% +1.50 ´ FGDP + 0.50 ´ FS +1% If it was the case that the rate of GDP growth was expected to be 4%, but in fact was 1%, then FGDP = Surprise in the rate of GDP growth = actual – expected = 1% – 4% = – 3% R = R - 2.30 ´ 5% +1.50 ´ ( -3%) + 0.50 ´ FS +1%
11.2 Risk: Systematic and Unsystematic
• A systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree. • An unsystematic risk is a risk that specifically affects a single asset or small group of assets.
• Now let us consider what happens to portfolios of stocks when each of the stocks follows a one-factor model. • We will create portfolios e the systematic risk with a 1-factor model.
R = R +U becomes R = R +m +ε

Nonsystematic Risk; Systematic Risk; m
where m is the systematic risk ε is the unsystematic risk
n
11.3 Systematic Risk and Betas
Systematic Risk and Betas: Example
R = R - 2.30 ´ 5% +1.50 ´ ( -3%) + 0.50 ´ FS +1% If it was the case that dollar-euro spot exchange rate, S($,€), was expected to increase by 10%, but in fact remained stable during the time period, then FS = Surprise in the exchange rate = actual – expected
= 0% – 10% = – 10%
R = R - 2.30 ´ 5% +1.50 ´ ( -3%) + 0.50 ´ ( -10%) +1%
Systematic Risk and Betas: Example
R = R - 2.30 ´ 5% +1.50 ´ ( -3%) + 0.50 ´ FS +1%
• Unsystematic risk can be diversified away.
• Examples of systematic risk include uncertainty about general economic conditions, such as GNP, interest rates or inflation. • On the other hand, announcements specific to a company, such as a gold mining company striking gold, are examples of unsystematic risk.