## 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 ## 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**
## 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 ## 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 ## 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
## 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 : 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** = wi**bi** ## The beta of a portfolio of stocks is equal to the weighted average of their individual betas: **bp** = wi**bi** **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. ## 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.
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