Based on annual returns from 1926-2004

Based on annual returns from 1926-2004

• Based on annual returns from 1926-2004

• Avg. Return Std Dev.

• Small Stocks 17.5% 33.1%

• Large Co. Stocks 12.4% 20.3%

• L-T Corp Bonds 6.2% 8.6%

• L-T Govt. Bonds 5.8% 9.3%

• U.S. T-Bills 3.8% 3.1%

Risk: The Big Picture

• Risk: The Big Picture

• Expected Return

• Stand Alone Risk

• Portfolio Return and Risk

Risk is an uncertain outcome or chance of an adverse outcome.

• Risk is an uncertain outcome or chance of an adverse outcome.

• Concerned with the riskiness of cash flows from financial assets.

• Stand Alone Risk: Single Asset

• relevant risk measure is the total risk of expected cash flows measured by standard deviation .

Portfolio Context: A group of assets. Total risk consists of:

• Portfolio Context: A group of assets. Total risk consists of:

• Diversifiable Risk (company-specific, unsystematic)
• Market Risk (non-diversifiable, systematic)

• Small group of assets with Diversifiable Risk remaining: interested in portfolio standard deviation.

• correlation ( or r) between asset returns which affects portfolio standard deviation

Well-diversified Portfolio

• Well-diversified Portfolio

• Large Portfolio (10-15 assets) eliminates diversifiable risk for the most part.

• Interested in Market Risk which is the risk that cannot be diversified away.

• The relevant risk measure is Beta which measures the riskiness of an individual asset in relation to the market portfolio.

HPR = (End of Period Price - Beginning Price + Dividends)/Beginning Price

• HPR = (End of Period Price - Beginning Price + Dividends)/Beginning Price

• HPR = Capital Gains Yield + Dividend Yield

• HPR = (P1-P0)/P0 + D/P0

• Example: Bought at $50, Receive $3 in dividends, current price is $54

• HPR = (54-50+3)/50 = .14 or 14%

• CGY = 4/50 = 8%, DY = 3/50 = 6%

Expected Rate of Return given a probability distribution of possible returns(ri): E(r)

• Expected Rate of Return given a probability distribution of possible returns(ri): E(r)

• n

• E(r) = Pi ri

• i=1

• Realized or Average Return on Historical Data:

• - n

• r = 1/n  ri

• i=1

Relevant Risk Measure for single asset

• Relevant Risk Measure for single asset

• Variance = 2 =  ( ri - E(r))2 Pi

• Standard Deviation = Square Root of Variance

• Historical Variance = 2 = 1/n(ri – rAVG )2

• Sample Variance = s2 = 1/(n-1) (ri – rAVG )2

Most investors are Risk Averse, meaning they don’t like risk and demand a higher return for bearing more risk.

• Most investors are Risk Averse, meaning they don’t like risk and demand a higher return for bearing more risk.

• The Coefficient of Variation (CV) scales risk per unit of expected return.

• CV = /E(r)

• CV is a measure of relative risk, where standard deviation measures absolute risk.

MAD Inc.

• MAD Inc.

• E(r) = 33.5%

• = 34.0%

• CV = 34%/33.5%

• CV = 1.015

E(rp) = wiE(ri) = weighted average of the expected return of each asset in the portfolio

• E(rp) = wiE(ri) = weighted average of the expected return of each asset in the portfolio

• In our example, MAD E(r) = 33.5% and CON E(r) = 7.5%

• What is the expected return of a portfolio consisting of 60% MAD and 40% CON?

• E(rp) = wiE(ri) = .6(33.5%) + .4(7.5%) = 23.1%

Looking at a 2-asset portfolio for simplicity, the riskiness of a portfolio is determined by the relationship between the returns of each asset over different states of nature or over time.

• Looking at a 2-asset portfolio for simplicity, the riskiness of a portfolio is determined by the relationship between the returns of each asset over different states of nature or over time.

• This relationship is measured by the correlation coefficient( r ): -1<= r < =+1

• All else constant: Lower r = less portfolio risk

Each MAD-CON ri = .6(MAD)+.4(CON);

• Each MAD-CON ri = .6(MAD)+.4(CON);

• E(Rp) = 23.1%

As more and more assets are added to a portfolio, risk measured by  decreases.

• As more and more assets are added to a portfolio, risk measured by  decreases.

• However, we could put every conceivable asset in the world into our portfolio and still have risk remaining. (See Fig. 8-8, pg. 265)

• This remaining risk is called Market Risk and is measured by Beta.

Beta(b) measures how the return of an individual asset (or even a portfolio) varies with the market.

• Beta(b) measures how the return of an individual asset (or even a portfolio) varies with the market.

• b = 1.0 : same risk as the market

• b < 1.0 : less risky than the market

• b > 1.0 : more risky than the market

• Beta is the slope of the regression line (y = a + bx) between a stock’s return(y) and the market return(x) over time, b from simple linear regression.

• Sources for stock betas: ValueLine Investment Survey (at BEL), Yahoo Finance, MSN Money, Standard & Poors

The story is the same as Chapter 6: a stock’s required rate of return = nominal risk-free rate + the stock’s risk premium.

• The story is the same as Chapter 6: a stock’s required rate of return = nominal risk-free rate + the stock’s risk premium.

• The main assumption is investors hold well diversified portfolios = only concerned with market risk.

• A stock’s risk premium = measure of market risk X market risk premium.

RPM = market risk premium = rM - rRF

• RPM = market risk premium = rM - rRF

• RPi = stock risk premium = (RPM)bi

• ri = rRF + (rM - rRF )bi

• = rRF + (RPM)bi

What is Intel’s required return if its B = 1.2 (from ValueLine Investment Survey), the current 3-mo. T-bill rate is 5%, and the historical US market risk premium of 8.6% is expected?

• What is Intel’s required return if its B = 1.2 (from ValueLine Investment Survey), the current 3-mo. T-bill rate is 5%, and the historical US market risk premium of 8.6% is expected?

The beta of a portfolio of stocks is equal to the weighted average of their individual betas: bp = wibi

• The beta of a portfolio of stocks is equal to the weighted average of their individual betas: bp = wibi

• Example: What is the portfolio beta for a portfolio consisting of 25% Home Depot with b = 1.0, 40% Hewlett-Packard with b = 1.35, and 35% Disney with b = 1.25. What is this portfolio’s required (expected) return if the risk-free rate is 5% and the market expected return is 14%?

AT&T currently sells for $36.50. Should we add AT&T with an expected price and dividend in a year of $39.54 & $1.42 and a b = 1.2 to our portfolio?

• AT&T currently sells for $36.50. Should we add AT&T with an expected price and dividend in a year of $39.54 & $1.42 and a b = 1.2 to our portfolio?

• To make our decision find AT&T’s expected return using the holding period return formula and compare to AT&T’s SML return.

• Recall that rRF = 5% and rM = 14%

A graphical representation of the CAPM/SML equation.

• A graphical representation of the CAPM/SML equation.

• Gives required (expected) returns for investments with different betas.

• Y axis = expected return, X axis = beta

• Intercept = risk-free rate = 3-month T-bill rate (B = 0)

• Slope of SML = market risk premium

• For the following SML graph, let’s use a 3-month T-bill rate of 5% and assume investors require a market return of 14%.

• Graph r = 5% + B(14%-5%)

• Market risk premium = 14% - 5% = 9%

What happens if inflation increases?

• What happens if inflation increases?

• What happens if investors become more risk averse about the stock market?

• Check out the following graphs with our base SML = 5% + (14%-5%)b

There are two functions in Excel that will find the X coefficient (beta).

• There are two functions in Excel that will find the X coefficient (beta).

• The functions are LINEST and SLOPE.

• The format is =LINEST(y range,x range)

• The above format is the same for SLOPE.

• Remember the stock’s returns is the y range, and the market’s returns is the x range.