1 Lecture 11: U ncertainty Supplementary stuff about uncertainty

2 Financial choices are about: Timing Risk-return tradeoff

3 Uncertainty risk and uncertainty, a bad thing? possible loss or gains in the future. e.g. a firm may make a fortune or go bankruptcy most investors are risk-averse

4 Risks for bond holders interest rate risk: in the future, i P, the possibility that sell at a loss before maturity. long-term bonds are more sensitive to interest rate risk. default risk risk of inflation  real rate of return may drop

5 Risk-return tradeoff Given a certain level of return, investor want to hold securities with the lowest risk. Given a certain level of risk, investor want to hold securities with the highest rate of return. In a diagram of risk and return, the optimal choices of securities (or portfolio of securities) are on a curve slope upwards: to earn a higher return you need to bear more risk; to avoid risk, you could only earn a lower rate of return – risk return tradeoff.

6 risk return efficient portfolio frontier

7 Expected return and risk Suppose return R, can take N values in the future: R 1, R 2,..., R N, with probabilities π 1, π 2,..., π N, respectively. Then the ‘average’ of return, i.e. expected return is measured by ‘mean’ of R: risk is measured by variance or standard deviation

8 Example investment outcome is uncertain: expected returns: E(Rp)=0; E(Rc)=0.1 risk (measured by s.d) S.d(Rp)=0.15; S.d(Rc)=0.1 Coke stock is more attractive. A portfolio of 40% Pepsi + 60% Coke yields a risk-free return of scenariossuccessfail probability0.5 Pepsi return Coke return00.2

9 Diversification Bottom Line: by holding several risky assets, risk can be reduced (diversi fi cation) Expect to see people spreading wealth across many assets How `good' an asset looks depends not only on own risk and return but also how it is correlated with other assets in the portfolio For example, emerging markets are attractive because of low correlation with US index