1. Risk and Return Risk and return defined –Average return –Total (absolute) risk –Total (relative) risk Portfolio risk and diversification effect Systematic Vs. non-systematic risk Beta and “reward to risk” CAPM

3. Return The additional cents on the dollar invested… k=(profit+additional cash flows)/initial investment Over a period of time…average return Arithmetic Return: Geometric Return: Why do returns matter? –$ does not mean much…alone –Cross-comparison between markets –Are “normally distributed”

4. Risk We need to think in terms of estimates in an uncertain world: Estimate=average return +/- some volatility Uncertainty or volatility of returns Standard deviation of returns Measured in % What does it mean?

7. Risk and Return How to compare assets? Which one do you pick? What is the problem here?

8. Think… Goal: FUN Choice 1: Orlando (3 theme parks) Choice 2: Hampshire (biggest inflatable bouncy castle) You equal utility for any of these attractions... Trick: There is one chance on two that each attraction will be closed There is one chance on two that Indianapolis Airport will be closed 1.Which one do you pick? 2.Think about the risks of not having fun, which one really matters?

9. Portfolio effect Portfolio Return is the weighted average return of each asset in the portfolio Portfolio Risk is not the weighted average risk of each asset in the portfolio. Portfolio risk has to do with each asset’s weight and risk, but also the degree to which they move together (ρ)

10. Mathematical Explanation

11. Portfolio risk and return…in English Portfolio return= (weighted) average assets’ return Portfolio risk = (weighted) average assets’ risk -(weighted) average assets prices’ propensity to move in opposite direction Or Portfolio risk = (weighted) average assets’ risk - Benefits from diversification

13. Risk and Diversification Announcements and news contain both an expected component and a surprise component; it is the surprise component that affects a stock’s price and therefore its return. Return=expected+unexpected Risk (return)= 0 + market risk + business risk The trick: if you hold many securities, the particularities of each security becomes irrelevant…thus, in a well diversified portfolio business- specific risk is irrelevant!

16. Risk that matters… If only market risk matters, then the risk premium of a security should be related (somehow) to the market risk premium! Let’s assume that those risk premiums are proportional: security risk premium=β x market risk premium This β is a multiplier which has to do with the relative risk premium of a security to the market risk premium…it is a relative Market (systematic) Risk

17. CAPM k i =k RF + k RP, then… –Security risk premium = (k i - k RF ) –Market risk premium = (k m - k RF ) If security risk premium=β x market risk premium Then, (k i - k RF) =β x (k m - k RF ) That is, k i = k RF +β x (k m - k RF ) This is also known as the SML (market equilibrium), a component of the CAPM As a result, any security’s return can calculated using β, k RF, and k m

20. Some Questions What if the observed returns are different from the theoretical returns? What is the market “relative” risk (β)? What does a β of 2 mean? What does a β of.5 mean? What does a β of –1 mean? How do we measure β? What is the β of a portfolio? Impact of inflation and risk aversion on expected returns