1. CHAPTER SEVEN Risk, Return, and Portfolio Theory J.D. Han

2. Learning Objectives 1. Define the term “market risk” and explain how it is related to expected return of a single financial asset. 2. Measure the risk in portfolio of multiple assets 3. Identify the main aims of diversification, and explain the principle benefits of international versus domestic diversification.

3. Risk? Default Risk; Credit Risk – all kinds of financial instruments (bonds, loans, stocks) Inflation Risk – only bonds Market Risk – all kinds of financial instruments “the chance that the actual outcome from an investment will differ from the expected outcome”

4. How to measure Market Risk of Individual Asset? 1. Variability= Deviation from its own Average Rate of Return “Mean Variance Approach” 2. Co-movement with the Market Index = Relative Variability of Rate of Return to the Market Index “Capital Market Pricing Model”

5. Rate of Return Recall that the rate of return is calculated by : Where: CF t = cash flows during the measurement period t P E = Final price at the end of period t or sale price P B = purchase price of the asset PC = change in price during the period

6. Calculating Mean Expected return – is the average of all possible return outcomes, where each outcome is weighted by the probability of its occurrence Where: E( R)= the expected return on a security R i = the i th possible return pr i = the probability of the i th return R i m = the # of possible returns

7. Variance- SD: Calculating Risk Variance or standard deviation is typically used to calculate the total risk associated with the expected return Variance = Standard deviation =

8. Numerical Examples: How to calculate the variance and the standard deviation? 1) Data of r over 3 years: 4%, 6%, and 8% E (r ) = (4 + 6 + 8)/3 = 6%           Data r: 3 times of 4, 5 times of 6, twice of 8

9. Now Mixing Multiple Assets in a Portfolio So far, we have examined Single Asset Case. How about the return and risk of Multiple Assets in an Investment Portfolio?

10. Portfolio’s Expected Return The expected return is calculated as a weighted average of the individual securities’ expected returns The combination portfolio must add up to be 100 percent Where: E(R p ) = the expected return on the portfolio w i = the portfolio weight for the i th security E(R i ) = the expected return on a single asset, or the i th security n = the # of different securities in the portfolio

11. Portfolio Risk Portfolio risk is less than the weighted average of the risk of the individual securities in a portfolio of risky securities unless their correlation coefficient is equal to one or they are perfectly positively correlated,where  p is risk of portfolio and  i is risk of a single asset i

12. Portfolio Risk  Portfolio Risk  p Two factors must be considered in developing an equation that will measure the risk of a portfolio through variance and standard deviation 1.Weighted individual security risks  1.,  2 … 2. Weighted co-movements between securities’ returns  1 2,    2 3 …. - measured by the correlations between the securities’ returns weighted again by the percentage of investable funds placed in each security

13. Covariance and Correlation Coefficient  = covariance between securities A and B R A,I = one estimated possible return on security A E(R A ) =mean value; most likely result m = the # of likely outcomes for a security for the period pr i = the probability of attaining a given return R A,i

14. Portfolio Risk Correlation coefficient – is a statistical measure of the relative co-movement between the return on securities A and B The relative measure is bound between +1.0 and –1.0 with  AB = +1.0 = perfect positive correlation  AB = - 0.0 = zero correlation  AB = -1.0 = perfect negative correlation

15. *The expected rate of return and standard deviation of the portfolio should be:Two Asset Portfolio Case Asset A ~(Er A,  A ) and Asset B ~ (Er B,  B ) Suppose we mix A and B at ratio of w1 to w2 for a portfolio P ~ (Er P,  p ) Return : Er p = w1 Er A, + w2 Er B Risk: *  AB is the correlation coefficient of r A and r B.

16. Diversification Through diversification non-systematic risk can be eliminated Systematic risk cannot be eliminated Total risk = non-systematic risk + systematic risk Diversification can be performed: 1. Domestically 2. Internationally

17. Summary 1.Uncertainly can be quantified in terms of probabilities, and risk is commonly associated with the variance or standard deviation of probability distributions. 2.When securities are combined, the combined risk of the resulting portfolio depends not only on the individual risk of the underlying securities but also on the statistical correlation that exists between the individual returns. 3.Correlation coefficients of +1, 0, and –1 indicate perfect positive correlation, statistical independence, and perfect negative correlation respectively.

18. Summary 4.Portfolio diversification reduces risk, and most investors hold diversified portfolios. 5.Diversification enables the reduction of risk through the elimination of company-specific or unique risk. Because the returns of most securities are related to the general state of the economy, they are positively correlated with each other. 6.International diversification offers additional benefits in terms of risk reduction.