1. Introduction to risk and return7
Introduction to risk and return

2. Figure 7.1 The Value of an Investment of $1 in 1900
One dollar invested in the common stock portfolio in 1900 would have grown to $14,276 in Similarly in the case of government bonds it would be $241 and in the case of T-bills it would be $71. Point out the fluctuation in stocks to begin the discussion of risk.

3. Figure 7.2 The Value of an Investment of $1 in 1900, real returns
This provides the same information as Slide 3 but adjusted for inflation.

4. Figure 7.3 Average Market risk premiums
Market risk premium = market rate of return – risk-free rate. Market risk premiums for various countries are given in an ascending order.

5. Figure 7.4 dividend yields in the u.s.
This shows that dividend yield has reduced considerably over time.

6. Figure 7.5 Stock market index returns
Stock returns have varied considerably over time. The graph of annual stock market returns indicates that negative returns occur approximately 25% of the time.

7. Figure 7.6 histogram of annual stock market returns
The histogram, of annual stock market returns, shows that negative returns have occurred approximately 25% of the time.

8. 7-2 measuring portfolio risk
Variance
Average value of squared deviations from mean; measures volatility
Standard Deviation
Square root of variance; measures volatility
Standard deviation is the square root of variance. Variance is the average value of squared deviations from mean. Variance can only be positive. This is how we measure risk in finance. Spend time BEFORE showing this slide asking students, “How do you define risk?” Rarely will someone define it as variance.

9. Table 7.2 coin-tossing game
This shows how to calculate the variance and standard deviation for a single security.

10. 7-2 measuring portfolio risk
This is the generic formula for return on a two-asset portfolio. It is a simple weighted average.

11. Figure 7.7 equity market risk
Equity market risk, as measured by the standard deviation of annual returns for various countries, is given in ascending order. What insights can be gained from those countries with higher risk and those with lower risk?

12. FIGURE 7.8 ANNUALIZED STANDARD DEVIATION OF DJIA OVER PRECEDING 52 WEEKS, 1900-2011
Annualized standard deviation, measured over the preceding 52 weeks, for DJIA from 1900–2008 is given. It shows that the standard deviation has declined over time. Offer an explanation or ask the students to do the same.

13. 7-2 measuring portfolio risk
Diversification
Strategy designed to reduce risk by spreading the portfolio across many investments
Unique Risk
Risk factors affecting only that firm; also called “diversifiable risk”
Market Risk
Economy-wide sources of risk that affect the overall stock market; also called “systematic risk”
Cover the definition of risk and how to reduce it. Total risk = market risk + unique risk. Provide a common-sense example of diversification and an example of non-diversification. A good example of diversification would be one restaurant stock and one grocery-store stock. They are complementary, but people must still eat. Thus, they provide diversification. Then discuss owning 30 film manufacturers and discuss that this would not be diversification since they are all in the same industry. The advent of digital technology would have negatively affected the whole portfolio.

14. Figure 7.10 comparing returns
Unlike risk, which can be reduced via diversification, show how returns are merely an average.

15. Figure 7.11 diversification eliminates specific risk
This is a graphical representation of the effect of diversification on total risk. By forming portfolios one can reduce risk through diversification. Total risk can be bifurcated into unique risk and market risk. Unique risk can be diversified away by forming portfolios.

16. Figure 7.12 variance of a two-stock portfolio
Variance of two-stock portfolio is sum of four boxes
Now present the case of a two-asset portfolio. This is a very intimidating slide for most students.
Portfolio variance = sp2 = x12s12 + x22s22 + (2)(x1)(x2)(s1)(s2)(r12) [where: x1 + x2 = 1]

17. 7-3 calculating portfolio risk
Example
Invest 60% of portfolio in Heinz and 40% in ExxonMobil. Expected dollar return on Campbell Soup stock is 6% and 10% on Boeing. Expected return on portfolio is:
By changing the proportion of funds invested in each stock, risk–return characteristics of the portfolio can be changed. Suppose you invest 60% of funds in Campbell’s and 40% in Boeing. Then calculate average return.

18. 7-3 calculating portfolio risk
Example
Invest 60% of portfolio in Heinz and 40% in ExxonMobil. Expected dollar return on Heinz stock is 6% and 10% on ExxonMobil. Standard deviation of annualized daily returns are 14.6% and 21.9%, respectively. Assume correlation coefficient of 1.0 and calculate portfolio variance.
Assume a correlation coefficient of one. Suppose you invest 60% of funds in Campbell’s and 40% in Boeing. Then your standard deviation can be calculated. Explain the definition of a correlation coefficient.

19. 7-3 calculating portfolio risk
Example
Invest 60% of portfolio in Heinz and 40% in ExxonMobil. Expected dollar return on Heinz stock is 6% and 10% on ExxonMobil . Standard deviation of annualized daily returns are 14.6% and 21.9%, respectively. Assume correlation coefficient of 1.0 and calculate portfolio variance.
This continues the previous example by showing the math behind standard deviation. You may need to refresh student memories on basic math.

20. 7-3 calculating portfolio risk
These are the equations for calculating the expected return and the variance for a two-asset portfolio. These equations are for reference only, as the prior slides cover them in depth.

21. 7-3 calculating portfolio risk
Example Correlation Coefficient = .4
Stocks s % of Portfolio Average Return
ABC Corp % %
Big Corp % %
Standard deviation = weighted average = 33.6
Standard deviation = portfolio = 28.1
Real standard deviation:
= (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4)
= 28.1
Return: r = (15%)(.60) + (21%)(.4) = 17.4%
The goal of this slide is to show how diversification reduces risk relative to a simple weighted average of standard deviations. The math is a simplified version of the prior slides, but the goal is not to teach math. The goal here is to compare the risk with and without diversification benefits. Note the return is still only a weighted average.

22. 7-3 calculating portfolio risk
Example, continued
Adding a third company to the portfolio: Correlation Coefficient = .3
Stocks s % of Portfolio Avg Return
Portfolio % %
New Corp % %
Standard deviation = weighted average = 31.80
Standard deviation = portfolio =
NEW return = weighted average = portfolio = 18.20%
Higher return, lower risk through diversification
The results are summarized. At this point, compare the 33.6 and Note the reduction in risk comes from diversification. Ask “can we reduce risk even more by adding another stock?”
There is no need to repeat the math. By showing the final results and comparing the with 23.43, again note the marginal reduction in risk. You can explain how additional diversification reduces risk. Reference back to the chart that showed reduced unique risk and decreasing marginal benefits. Remind students that diversification cannot reduce market risk. We have achieved higher return and lower risk. This is because of diversification.

23. Figure 7.13 Portfolio variance
Shaded boxes contain variance terms
Unshaded boxes contain covariance terms 1 2 3 4 5 6 N
To calculate portfolio variance, add up the boxes
STOCK
This is the logical extension to an N-asset portfolio. You need a computer to solve for N-asset portfolios. There are N variance terms and [N(N-1)/2] covariance terms.
STOCK

24. 7-4 how individual securities affect portfolio risk
Market Portfolio
Portfolio of all assets in economy
Usually uses broad stock market index to represent market
Beta
Sensitivity of stock’s return to return on market portfolio
Market portfolio is a value-weighted portfolio of all the assets in the economy. Beta is a relative measure of risk. Beta of the market portfolio is one. Beta is a measure of market risk. Beta represents the sensitivity of a stock’s return to the return on the market portfolio.

25. Figure 7.14 returns on ford
Return on stock changes on average by 1.53% for each additional 1% change in market return
Beta = 1.53
Return on Ford, %
Return on market, %
Beta is the slope of the regression line. Market return is on the x-axis and stock return on the y-axis. Beta can be calculated using statistical functions in a financial calculator.

26. FIGURE 7.15 beta
The slide provides a more precise illustration of the diminishing marginal benefit of diversification concept. It also shows how average betas have risk reduction characteristics.

27. 7-4 how individual securities affect portfolio risk
Beta Formula
: covariance with market
: variance of market
This equation is useful for estimating beta. The ratio of covariance to variance measures a stock’s contribution to portfolio risk. Beta (β) = σim/(σm2)
Beta (β) = σim/(σm2)
σim = covariance with the market
σm2 = variance of the market
Explain that the covariance of the market with itself is the same as the variance of the market. Thus, the beta of the market is always 1.0.

28. Table 7.7 calculating variance and covariance
This frame shows how beta is calculated using historical data (monthly returns data).
Calculator solution: X1 = -8%; X2 = 4%; X3 = 12%; X4 = -6%; X5 = 2%; X6 = 8%;
Y1 = -11%; Y2 = 8%; Y3 = 19%; Y4 = -13%; Y5 = 3%; Y6 = 6%;
beta = 1.5