1. Investing 101 Lecture 4 Basic Portfolio Building

2. Review Explain supply and demand? Explain supply and demand? What is GDP? What is GDP? What are Consumer/Producer surplus? Reservation Price? What are Consumer/Producer surplus? Reservation Price? What is an interest rate? What is an interest rate? What is an exchange rate? What is an exchange rate?

3. Does anyone have anything to share? Stock update? Stock update? Anything special happening in life? Anything special happening in life? Anyone have any questions on unrelated random financial topics? Anyone have any questions on unrelated random financial topics? I don’t expect to get through all of today’s material in two hours, may stay 15 min and/or go into next day. I don’t expect to get through all of today’s material in two hours, may stay 15 min and/or go into next day.

4. Main Teaching Points Variance and standard deviation Variance and standard deviation Security market line (SML) Security market line (SML) Capital allocation line (CAL) Capital allocation line (CAL) Capital assets pricing model (CAPM) Capital assets pricing model (CAPM) Covariance and correlation Covariance and correlation Diligent asset allocation Diligent asset allocation Pulling it all together. Pulling it all together.

5. Warning There are lots of slides in today’s class. There are lots of slides in today’s class. Many of them are pictures and graphs. Many of them are pictures and graphs. If you are a spatial mathematician you will want to pay close attention. If you are a spatial mathematician you will want to pay close attention. There are some eqns you do NOT have to understand them, so if they confuse you do your best to block them out. There are some eqns you do NOT have to understand them, so if they confuse you do your best to block them out. Lets get started we have A LOT to learn and much to pull together. Lets get started we have A LOT to learn and much to pull together.

6. All the stats you will ever need to know

7. Empirical Rule Has anyone heard of it??? Has anyone heard of it??? 68 95 99 68 95 99 The key to risk in stocks. The key to risk in stocks.

8. The Security Market Line Risk Return SBUX GOOG TELUS Risk Free

9. Asset Allocation Asset Allocation is the portfolio choice among broad investment classes: Asset Allocation is the portfolio choice among broad investment classes: One risky asset and one risk-free asset One risky asset and one risk-free asset Two risky assets Two risky assets Two risky assets and one risk-free asset Two risky assets and one risk-free asset Many risky assets and one risk-free asset Many risky assets and one risk-free asset

10. Asset Classes Risky Assets Risky Assets Stocks (S&P Comp. Index) Stocks (S&P Comp. Index) Mean Real Return: 10% Mean Real Return: 10% Standard Deviation: 20% Standard Deviation: 20% Bonds Bonds Mean Real Return: 4% Mean Real Return: 4% Standard Deviation: 10% Standard Deviation: 10% Correlation with Real Stock Return: 0.2 Correlation with Real Stock Return: 0.2 T-Bills (Risk-free asset) T-Bills (Risk-free asset) Real Return: 1% Real Return: 1%

11. Portfolio of Risk-Free Asset and Risky Asset What is the expected return and the standard deviation of a portfolio that invests: What is the expected return and the standard deviation of a portfolio that invests: w in stocks w in stocks 1-w in the risk-free asset? 1-w in the risk-free asset?

12. Capital Allocation Line Expected Return of Portfolio: Expected Return of Portfolio: Standard Deviation of Portfolio: Standard Deviation of Portfolio: Substituting for w, gives the Capital Allocation Line (CAL): Substituting for w, gives the Capital Allocation Line (CAL):

13. Capital Allocation Line  r  E(r) 0 P r f

14. Capital Allocation Line  r  E(r) 0 P r f Slope = E (r p ) - r f  r p  The Capital Allocation Line

15. Capital Allocation Line

16. The Capital Allocation Line shows the risk- return combinations available by changing the proportion invested in a risk-free asset and a risky asset The Capital Allocation Line shows the risk- return combinations available by changing the proportion invested in a risk-free asset and a risky asset The slope of the CAL is the reward-to- variability ratio The slope of the CAL is the reward-to- variability ratio

17. Capital Assets Pricing Model Now that we know that different stocks hold different levels of risk, we can use this knowledge to price the stocks. Now that we know that different stocks hold different levels of risk, we can use this knowledge to price the stocks. We use CAPM to find the rate at which to discount the future dividends of a stock. We use CAPM to find the rate at which to discount the future dividends of a stock. Perpetuity stock = D1/k Perpetuity stock = D1/k Growth stock = D1/k-g Growth stock = D1/k-g Where D = dividend, g = growth, k = discount rate. Where D = dividend, g = growth, k = discount rate.

18. CAPM Equation k = rf + B(Rm-rf) k = rf + B(Rm-rf) Where rf = Risk free rate Rm = Return of the market and B = beta. Where rf = Risk free rate Rm = Return of the market and B = beta. Beta is the correlation b/w the returns of the market and the returns of the stock. Beta is the correlation b/w the returns of the market and the returns of the stock.

19. RMkt R stock

20. Risk Aversion Now the question is, which risk-return combination along the CAL do you want? Now the question is, which risk-return combination along the CAL do you want? To answer this we need to bring your preferences for risk into the picture To answer this we need to bring your preferences for risk into the picture We will use indifference curves to represent risk aversion We will use indifference curves to represent risk aversion Indifference curves represent utility functions Indifference curves represent utility functions

21. Indifference Curves  r  E(r) 0 u=3 u=2 u=1 A B C Surrey N Van

22. Asset Allocation Now we can combine the indifference curves with the capital allocation line Now we can combine the indifference curves with the capital allocation line If investors are maximizing their utility, they will choose the highest possible indifference curve If investors are maximizing their utility, they will choose the highest possible indifference curve The highest curve is tangent to the CAL The highest curve is tangent to the CAL

23. Asset Allocation  r  E(r) 0 P f CAL IndifferenceCurves r

24. Portfolio Frontier with Stocks and Bonds

25. Portfolio Frontier The portfolio frontier depicts the feasible portfolio choices for investors holding stocks and bonds The portfolio frontier depicts the feasible portfolio choices for investors holding stocks and bonds The minimum variance portfolio includes 86% bonds and 14% stocks The minimum variance portfolio includes 86% bonds and 14% stocks Portfolios below the minimum variance portfolio are inefficient Portfolios below the minimum variance portfolio are inefficient The portfolio frontier above the minimum variance portfolio is called ‘efficient frontier’ The portfolio frontier above the minimum variance portfolio is called ‘efficient frontier’

26. Correlation: Two Risky Assets To see the importance of correlation, we will look at the set of feasible portfolios under three different assumptions: To see the importance of correlation, we will look at the set of feasible portfolios under three different assumptions: 1) ρ AB = 1 1) ρ AB = 1 2) ρ AB = -1 2) ρ AB = -1 3) ρ AB = 0 3) ρ AB = 0 Then we will discuss the intermediate cases Then we will discuss the intermediate cases

27. Perfect Correlation  (r) E(r) 0 A B

28. Perfect Correlation  (r) E(r) 0 A B  AB = 1

29.  (r) E(r) 0 A B  AB = 1= 1= 1= 1  Perfect Negative Correlation AB = -1

30. No Correlation  (r) E(r) A B  AB = 1  AB = 0  AB = -1 0

31. Portfolio Frontiers with Different Asset Correlations

32. Asset Allocation with Risk-Free Asset Introducing a risk-free asset besides stocks and bonds improves the investment opportunities Introducing a risk-free asset besides stocks and bonds improves the investment opportunities

33. Capital Allocation Lines using Stocks and Bonds

34. Optimal Capital Allocation Line

35. Portfolio Frontier with Three Risky Assets

36. Portfolio Frontier with Many Risky Assets

37. Diversification “It is part of a wise man … not to venture all his eggs in one basket” “It is part of a wise man … not to venture all his eggs in one basket” - Miguel de Cervantes “Put all your eggs in one basket and watch that basket” “Put all your eggs in one basket and watch that basket” - Mark Twain

38. The Benefits of Diversification The variance of the return of a portfolio that includes N different assets depends on the weight w and on the covariances : The variance of the return of a portfolio that includes N different assets depends on the weight w and on the covariances :

39. Diversification The standard deviation of a portfolio tends to decrease as more risky assets are added to the portfolio The standard deviation of a portfolio tends to decrease as more risky assets are added to the portfolio Number of Securities Std. Deviation Of Portfolio Market Risk Firm-specific Risk

40. Questions?