Chapter 10. Chapter 10 Topics. Recent Rates

Transcription

1 Chapter 10 Introduction to Risk, Return, and the Opportunity Cost of Capital Chapter 10 Topics Rates of Return Risk Premiums Expected Return Portfolio Return and Risk Risk Diversification Unique & Market Risk Recent Rates 3-month Treasury Bill 2.69% 1-year Treasury Note 3.21% 5-year Treasury Note 3.90% 5-year AAA Corporate Bond 4.23% 10-year Treasury Bond 4.28% 10-year AAA Corporate Bond 4.82% Why are these rates different? 1

2 Yield Curves 6 5 Percent Treasury AAA-Corporate Years to Maturity Some Historical Risk & Return Perspective ( ) Investment Average Standard Portfolio Annual Return Deviation Treasury Bills 4.1% 2.8% Treasury Bonds 5.1% 8.2% Common Stocks 11.8% 19.9% Historical Risk Premium over T-bills: Treasury Bonds (Maturity Premium) = 5.1% - 4.1% = 1.0% Common Stock (Market) Risk Premium = 11.8% - 4.1% = 7.7% Market Indexes Dow Jones Industrial Average (The Dow) Value of a portfolio holding one share in each of 30 large industrial firms. Standard & Poor s Composite Index (The S&P 500) Value of a portfolio holding shares in 500 firms. Holdings are proportional to the number of shares in the issues. 2

3 Inflation and Interest Rates Inflation - Rate at which prices as a whole are increasing. Nominal Interest Rate - Rate at which money invested grows. Real Interest Rate - Rate at which the purchasing power of an investment increases. Inflation and Interest Rates 1 + real interest rate = 1+nominal interest rate 1+inflation rate approximation formula Real int. rate nominal int. rate - inflation rate Inflation, Nominal & Real Rates Example If the interest rate on one year govt. bonds is 5.0% and the inflation rate is 2.2%, what is the real interest rate? real interest rate = Savings Bond 1 + real interest rate = real interest rate =.027 or 2.7% Approximat ion = =.028 or 2.8% 3

4 Expected Return: Single Asset Expected Rate of Return given a probability distribution of possible returns (r i ): E(r) E(r) = Σ p i r i i=1 Realized or Average Return on Historical Data: - n r = 1/n Σ r i i=1 n Standard Deviation Relevant Risk Measure for single asset Variance = σ 2 = Σ p i (r i - E(r)) 2 Standard Deviation = Square Root of Variance Example: Exp. Return and σ State of Contrary Economy Probability MAD Inc. Co. (CON) Boom % -6% Normal % 10% Recession % 20% 4

5 Example: Standard Deviation Portfolio Risk and Return E(r p ) = Σ w i E(r i ) = 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 70% MAD and 30% CON? Risk and Diversification Portfolio rate of return ( ( = + x )( x )( fraction of portfolio in first asset fraction of portfolio in second asset ) ) rate of return on first asset rate of return on second asset E(r p ) = Σ w i E(r i ) =.7(33.5%) +.3(7.5%) = 25.7% 5

6 Portfolio Risk 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 scenarios or over time. This relationship is measured by the correlation coefficient( ρ ): -1<= ρ < =+1 Lower ρ = less portfolio risk compared to the weighted average of the standard deviations. Example 70% MAD, 30% CON Portfolio σ State of Contrary MAD-CON Economy Probability MAD Inc. Co. (CON) Portfolio Boom % -6% 54.2% Normal % 10% 24.0% Recession % 20% -15.0% Risk and Diversification 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. 6

7 Risk and Diversification Portfolio standard deviation Number of Securities Risk and Diversification Portfolio standard deviation 0 Unique risk Market risk Number of Securities Market Risk As more and more assets are added to a portfolio, total risk measured by σ decreases. However, we could put every conceivable asset in the world into our portfolio and still have risk remaining. This remaining risk is called Market Risk and is measured by Beta (Chapter 11). 7