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# Inveatment analysis and portfolio management

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what is investment? what is rate of returns? how to measure risk?

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### Inveatment analysis and portfolio management

1. 1. o o o o Any investment involves a current commitment of funds for some period of time in order to derive future payments that will compensate for: the time the funds are committed (the real rate of return) the expected rate of inflation (inflation premium) uncertainty of future flow of funds (risk premium)
2. 2. o o EAR 1 HPR 1 N 1 o EAR = Equivalent Annual Return HPR = Holding Period Return N = Number of years
3. 3. AM = Arithmetic Mean AM R1 R2 ... RN N GM = Geometric Mean Ri = Annual HPRs N = Number of years GM 1 R1 1 R2 ... 1 RN 1 N 1
4. 4. o The mean historical rate of return for a portfolio of investments is measured as the weighted average of the HPRs for the individual investments in the portfolio, or the overall change in the value of the original portfolio
5. 5. o o Risk is the uncertainty whether an investment will earn its expected rate of return Probability is the likelihood of an outcome n E(R i ) (Probabilit y of Return) i 1 n (Pi )(R i ) i 1 (Possible Return)
6. 6. o o Much of modern finance is based on the principle that investors are risk averse Risk aversion refers to the assumption that, all else being equal, most investors will choose the least risky alternative and that they will not accept additional risk unless they are compensated in the form of higher return
7. 7. n HPR i 2 E HPRi i 1 N 2 Where: = Variance (of the pop) HPR = Holding Period Return i E(HPR)i = Expected HPR* N = Number of years
8. 8. n 2 (Pi ) R i E(R) 2 i 1 = Variance Note: Because we multiply by the probability of each return occurring, we do NOT divide by N. If each probability is the same for all returns, then the variance can be calculated by either multiplying by the probability or dividing by N. Ri = Return in period i E(R) = Expected Return Pi = Probability of Ri occurring
9. 9. n Pi [R i -E(R i )]2 i 1 n Pi [R i -E(R i )]2 i 1 1 2 Standard Deviation is a measure of dispersion around the mean. The higher the standard deviation, the greater the dispersion of returns around the mean and the greater the risk.
10. 10. o o Coefficient of variation (CV) is a measure of relative variability CV indicates risk per unit of return, thus making comparisons easier among investments with large differences in mean returns
11. 11. o Three factors influence an investor’s required rate of return oReal rate of return oExpected rate of inflation during the period oRisk
12. 12. oAssumes no inflation. oAssumes no uncertainty about future cash flows. oInfluenced by the time preference for consumption of income and investment opportunities in the economy
13. 13. 1 Nominal 1 Real 1 Expected Inflation The nominal risk free rate of return is dependent upon: Conditions in the Capital Markets Expected Rate of Inflation
14. 14. o Five factors affect the standard deviation of returns over time. oBusiness risk: oFinancial risk oLiquidity risk oExchange rate risk oCountry risk
15. 15. oUncertainty of income flows caused by the nature of a firm’s business oSales volatility and operating leverage determine the level of business risk. o Uncertainty caused by the use of debt financing. o Borrowing requires fixed payments which must be paid ahead of payments to stockholders. o The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium.
16. 16. o the uncertainty introduced by the secondary market for an investment. o How long will it take to convert an investment into cash? o How certain is the price that will be received? o o the uncertainty 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.
17. 17. o o Country risk (also called political risk) refers to 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
18. 18. Frank K. Reilly & Keith C. Brown REFERENCE