Presentation on theme: "The Trade-off between Risk and Return"— Presentation transcript:
1The Trade-off between Risk and Return Professor ThomsonFin 3013
2A trade-off always arises between expected risk and expected return. Risk and ReturnThe return earned on investments represents the marginal benefit of investing.Risk is one of the marginal costs of investing (the other is the pure time value of money).A trade-off always arises between expected risk and expected return.
3Risk and ReturnValuing risky assets - a task fundamental to financial managementThree-step procedure for valuing a risky asset1. Determine the asset’s expected cash flows2. Choose discount rate that reflects asset’s risk3. Calculate present value (PV cash inflows - PV outflows)The three-step procedure is calleddiscounted cash flow (DCF) analysis.
4Financial ReturnTotal return: the total gain or loss experienced on an investment over a given period of timeComponents of the total returnIncome stream from the investmentCapital gain or loss due to changes in asset pricesTotal return can be expressed either in dollar terms or in percentage terms.
5Cash Flow Time Line Pt-1 cash payments Pt Time t Time tPt = Price at time t (today)Capital Gain = Pt – Pt-1= Price today – Price last periodDollar Return = Cash Payments + Capital Gain= Cash Payments + Pt – Pt-1
6Example 6.1You purchased a stock last year for $25. It has paid $1 in dividends and is not worth $21. What is your Dollar Return?
7Example 6.2You bought an 11% coupon bond one year ago for $ You can sell that bond today for $ What is your Dollar Return?
8Holding Period Return (hpr) or Percentage Return This is the most common way to express the gains or losses over a periodIt is the $Return relative to the amount invested1+hpr is often called the wealth relative
9Example 6.1 (Revised)You purchased a stock last year for $25. It has paid $1 in dividends and is not worth $21. What is your Dollar Return?What is your hpr?
10Example 6.2 RevisedYou bought an 11% coupon bond one year ago for $ You can sell that bond today for $ What is your Dollar Return?What is your hpr?
11Measuring Wealth over Time Yearhpr$1 Investment$1 Investment each year115%1*(1.15) = 1.15Vt-1(1+it) = Vt1*(1.15)=1.15Vt-Vt- Vt-1 (1+it) = Vt2-10%1.15*(0.90) =1.035(1+1.15)*(0.90) = 1.935313%1.035*1.13 =( )*(1.13) =
12Arithmetic Average Return Add the individual hpr’s and divide by the number of years
13Geometric Rate of Return Multiply by the wealth relatives, raise to the 1/N power and subtract 1Is the constant rate of wealth building over time that results in the observed future valueBy Financial Calculator: P/YR=1I/YR(FV=1.1696, PV=-1, N=3) = 5.36%
14IRR from a Constant Investment P/YR=1tCF-11233.3166Press IRR = 5.10%
15Value of $1 Invested in Equities, Treasury Bonds and Bills,Year$15,579$148$61$2210,000100,0001,000100101Equities Bonds Bills Inflation
16Geometric Return Calculation A $1 investment in Large Stocks (with dividends reinvested) was worth after 103 years. The geometric mean return can be computed as (P/Yr = 1)I/YR(FV=15579, PV=-1, N=103)=9.83% StocksI/YR(FV=148, PV=-1, N=76)=4.97% Long US BondI/YR(FV=61, PV=-1, N=76)=4.07% US Treasury BillsI/YR(FV=22, PV=-1, N=76)=3.05% Inflation
17Geometric Real Rates of Return To compute the long run real rate of return one can divide the ending value of the investment by the ending value of the inflation figure to determine the purchasing power of the investment. Then compute the return using “Real Dollars”Real value of the Large Stocks at end of period is 15579/22 =I/YR(FV=708.14, PV=-1, N=103)=6.58%I/YR(FV=6.73, PV=-1, N=103)=1.87% Long US BondI/YR(FV=2.73, PV=-1, N=103)=1.00% TBill
24Take home messageIf you have a short holding period, stocks are very risky, but from a longer term perspective they have provided the best returns both recently and historicallyInvestment is not about saving money for the future, its about earning money from the money you invested so that most of your portfolio is from the earning of that portfolio and not from your deposits into that fund
25Percentage Returns on Bills, Bonds, and Stocks, 1900 - 2003 Difference between average return of stocks and bills = 7.6%Difference between average return of stocks and bonds = 6.5%Risk premium: the difference in returns offered by a risky asset relative to the risk-free return available
26Why are Treasury Bills considered risk free? If the government default on Treasury Bills, your last concern will be the money you might have earned on the TBWhen you buy a Treasury Bill, you purchase it at a discount and redeem it at par, so you know when you buy it, what your return will beIf you buy a stock, you don’t know what you will sell it for, or what dividends it will pay; thus, it is riskyThe yield on Treasury Bills, is generally taken to be the risk free return
27Distribution of Historical Stock Returns, 1900 - 2003 < to to to 0 to to to 30 to to >50-20-101020304050Percent return in a given yearProbability distribution for future stock returns is unknown. We can approximate the unknown distribution by assuming a normal distribution.
28Variability of Stock Returns Normal distribution can be described by its mean and its variance. A Normal Distribution is symmetric around the meanVariance (2) - the expected value of squared deviations from the meanUnits of variance (%-squared) - hard to interpret, so calculate standard deviation, a measure of volatility equal to square root of 2
30Volatility of Asset Returns Asset classes with greater volatility pay higher average returns.Average return on stocks is more than double the average return on bonds, but stocks are 2.5 times more volatile.
31Average Returns and St. Dev. for Asset Classes, 1900-2003 StocksBillsBondsStandard Deviation (%)Investors who want higher returns have to take more riskThe incremental reward from accepting more risk seems constant
32Average Return and St. Dev. for Individual Securities, 1994-2003 Average risk for all stocks in this period was 60%For various asset classes, a trade-off arises between risk and return. Does the trade-off appear to hold for all individual securities?
33Average Return and St. Dev. for Individual Securities, 1994-2003 Wal-MartAnheuser-BuschAmerican AirlinesArcher Daniels MidlandStandard Deviation (%)No obvious pattern here
34DiversificationMost individual stock prices show higher volatility than the price volatility of portfolio of all common stocks.How can the standard deviation for individual stocks be higher than the standard deviation of the portfolio?Diversification: investing in many different assets reduces the volatility of the portfolio.The ups and downs of individual stocks partially cancel each other out.
35The standard deviation of the portfolio is lower than the standard deviation of either Coke or Wendy’s
36The Impact of Additional Assets on the Risk of a Portfolio Number of StocksSystematic RiskPortfolio of 11 stocksAMDUnsystematic RiskAMD + American AirlinesAMD + American Airlines + Wal-MartPortfolio Standard Deviation
37Systematic and Unsystematic Risk Diversification reduces portfolio volatility, but only up to a point. Portfolio of all stocks still has a volatility of 21%.Systematic risk: the volatility of the portfolio that cannot be eliminated through diversification.Unsystematic risk: the proportion of risk of individual assets that can be eliminated through diversification, for example, by buying mutual funds. Because this risk can be eliminated, there is no reward for holding unsystematic riskWhat really matters is systematic risk….how a group of assets move together.
38Systematic and Unsystematic Risk Anheuser Busch stock had higher average returns than Archer-Daniels-Midland stock, with smaller volatility.American Airlines had much smaller average returns than Wal-Mart, with similar volatility.The tradeoff between standard deviation and average returns that holds for asset classes does not hold for individual stocks.Because investors can eliminate unsystematic risk through diversification, market rewards only systematic risk.Standard deviation contains both systematic and unsystematic risk.
39Risk and Return Investment performance is measured by total return. Trade-off between risk and return for assets: historically, stocks had higher returns and volatility than bonds and bills.One measure of risk: standard deviation (volatility)Unsystematic and (systematic) risk: risk that can (cannot) be eliminated through diversification, respectively
41Total dollar return = income + capital gain / loss Dollar ReturnsTotal dollar return = income + capital gain / lossTerrell bought 100 shares of Micro-Orb stock for $25A year later:Dividend = $1/shareSold for $30/shareDollar return = (100 shares) x ($1 + $5) = $600Owen bought 50 shares of Garcia Inc. stock for $15A year later:No dividends paidSold for $25/shareDollar return = (150 shares) x ($15)= $500
42Percentage ReturnsTerrell’s dollar return exceeded Owen’s by $100. Can we say that Terrell was better off?No, because Terrell and Owen’s initial investments were different: Terrell spent $2,500 in initial investment, while Owen spent $750.Percentage return: total dollar return divided by the initial investment
43Percentage ReturnsIn percentage terms, Owen’s investment performed better than Terrell’s did.