BF 320: Investment & Portfolio Management M.Mukwena

Investment Setting Objectives: Why do individuals invest? What is an investment? How do we measure the rate of return on an investment? How do investors measure risk related to alternative investments? What macroeconomic and microeconomic factors contribute to changes in the required rate of return for investments? M.Mukwena

Why Do Individuals Invest ? 2 choices with your earnings: Save and tradeoff present consumption for a larger future consumption Riskier option of investments M.Mukwena

Required Rate Of Return 1. The pure rate of interest is the exchange rate between future consumption and present consumption. Market forces determine this rate. Ex: if you can exchange K5 of certain income today for K50 tomorrow this rate is 5/50=10%. AKA pure time value of money M.Mukwena

Pure Rate of Interest M.Mukwena

Required Rate Of Return 2. If the future payment will be diminished in value because of inflation, then the investor will demand an interest rate higher than the pure time value of money to also cover the expected inflation expense. Ex: Investor in Zambia would expect 7% compensation for inflation M.Mukwena

Required Rate Of Return 3. If the future payment from the investment is not certain, the investor will demand an interest rate that exceeds the pure time value of money plus the inflation rate to provide a risk premium to cover the investment risk. Ex: A return of 2% Therefore from above examples an investor would need compensation of 10%+7%+2% =19% M.Mukwena

Defining an Investment A current commitment of money (K) for a period of time in order to derive future payments that will compensate for: ◦ the time the funds are committed ◦ the expected rate of inflation ◦ uncertainty of future flow of funds. These three make up required rate of return M.Mukwena

Measures of Historical Rates of Return Holding Period Return M.Mukwena

Measures of Historical Rates of Return M.Mukwena Holding Period Yield HPY = HPR = 0.10 = 10%

Measures of Historical Rates of Return M.Mukwena

Measures of Historical Rates of Return Arithmetic Mean M.Mukwena

Measures of Historical Rates of Return Geometric Mean M.Mukwena

Measures of Historical Rates of Return M.Mukwena Year Beginning Value of Investment End Value of Investment HPRHPY

Arithmetic Mean versus Geometric Mean InvbegY1Y2HPRHPYAMGM A102010Yr1:20/10=2 Yr2:10/20=0.5 Yr1: 2-1=1 Yr2: 0.5-1=-0.5 B10812Yr1: 8/10=0.8 Yr2: 12/8=1.5 Yr1: 0.8-1=-0.2 Yr2:1.5-1=0.5 M.Mukwena For A the AM is not true (25%) since investment went from 10 to 20 to 10. Therefore GM is better measure. For B: 10(1.15)(1.15)=13.23 which should be 12. However 10(1.0954)(1.0954)=12. Therefore GM is better measure

Portfolio of Investments The mean historical rate of return for a portfolio of investments is measured as the weighted average of the HPYs for the individual investments in the portfolio. Example to follow M.Mukwena

Computation of Holding Period Yield for a Portfolio M.Mukwena *Market Weights based on Beginning Mkt Value BeginBeginningEnding *MarketWtd. StockShares Price Mkt. Value Price Mkt. ValueHPRHPYWeightHPY A 100,000 K K % B 200,000 K K % C 500,000 K K % Total K K HPR = K =1.095 K HPY = =0.095 =9.5%

Expected Rates of Return Risk is uncertainty that an investment will earn its expected rate of return Probability is the likelihood of an outcome M.Mukwena

Risk Aversion The assumption that most investors will choose the least risky alternative, all else being equal and that they will not accept additional risk unless they are compensated in the form of higher return M.Mukwena

Probability Distributions Risk-free Investment M.Mukwena Probability Return

Probability Distributions Probability Distributions Risky Investment with 3 Possible Returns M.Mukwena Return Probability

Probability Distributions Probability Distributions Risky investment with ten possible rates of return M.Mukwena Probability

Measuring the Risk of Expected Rates of Return M.Mukwena

Measuring the Risk of Expected Rates of Return Standard Deviation is the square root of the variance M.Mukwena

Measuring the Risk of Expected Rates of Return Coefficient of variation (CV) a measure of relative variability that indicates risk per unit of return Standard Deviation of Returns Expected Rate of Returns M.Mukwena

Measuring the Risk of Expected Rates of Return Investment AInvestment B Expected Return Standard Deviation Coefficient of Variation0.05/0.07 = /0.12 = B has less risk per unit and is therefore better investment M.Mukwena

The Real Risk Free Rate (RRFR) ◦ Assumes no inflation. ◦ Assumes no uncertainty about future cash flows. ◦ Influenced by time preference for consumption of income and investment opportunities in the economy Take note: RRFR was earlier called pure time value of money as only sacrifice investor made was deferring use of money M.Mukwena

Nominal Risk-Free Rate Rate of interest stated in money terms Dependent upon ◦ Conditions in the Capital Markets ◦ Expected Rate of Inflation M.Mukwena

Adjusting For Inflation Nominal RFR = (1+Real RFR) x (1+Expected Rate of Inflation) – 1 Ex: If you require a real growth in the purchasing power of your investment of 8%, and you expect the rate of inflation over the next year to be 3%, what is the lowest nominal return that you would be satisfied with? (1+0.08) x (1+0.03) - 1 = M.Mukwena

Systematic Risk Business risk Financial risk Liquidity risk Exchange rate risk Country risk M.Mukwena

Systematic Risk Business Risk: Uncertainty of income flows caused by the nature of a firm’s business Sales volatility and operating leverage determine the level of business risk. Financial Risk: Uncertainty caused by the use of debt financing. AKA leveraging risk Borrowing requires fixed payments which must be paid ahead of payments to stockholders. The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium. Q: Does a company utilizing only common stock to finance their investments suffer financial risk? M.Mukwena

Systematic Risk Liquidity Risk: Uncertainty is introduced by the secondary market for an investment. How long will it take to convert an investment into cash? How certain is the price that will be received? Exchange Rate Risk: Uncertainty of return is introduced by acquiring securities denominated in a currency different from that of the investor. Changes in exchange rates affect the investors return when converting an investment back into the “home” currency. M.Mukwena

Systematic Risk Country Risk: Political risk is the uncertainty of returns caused by the possibility of a major change in the political or economic environment in a country. Individuals who invest in countries that have unstable political- economic systems must include a country risk-premium when determining their required rate of return f (Business Risk, Financial Risk, Liquidity Risk, Exchange Rate Risk, Country Risk) M.Mukwena

Systematic Risk The relevant risk measure for an individual asset is its co-movement with the market portfolio Systematic risk relates the variance of the investment to the variance of the market Beta measures this systematic risk of an asset M.Mukwena

Security Market Lines M.Mukwena (Expected)

Changes in the Required Rate of Return Due to Movements Along the SML M.Mukwena

Change in Market Risk Premium Change in Market Risk Premium M.Mukwena NRFR Expected Return Rm´Rm´ RmRm

Capital Market Conditions, Expected Inflation, and the SML M.Mukwena NRFR NRFR´ Expected Return