The risk and returns

Résumé du document

Rates of Return over Multiple Periods, typically quarters are expressed as: Arithmetic Average of the quarterly returns, is the total return divided by the number of quarters. It ignores the compounding effect. Geometric (time weighted) Average of the quarterly returns, is equal to the single period return that would give the same performance as the actual return of the multiple periods. It ignores the quarter to quarter variations in the value of the funds under management The geometric average is always less than the arithmetic average because it takes into account, compounding. This does not mean that the arithmetic average is not useful. The arithmetic average is probably a better predictor of future performance. When the time periods and/or returns are small, adding or averaging rates of returns will give similar answers as compounding them. The arithmetic or geometric average do not have to be used for annual averages only. They can be used for any period of any length. An annual length is one of the most common. Dollar Weighted Return considers investment as a Capital Budget problem of cash outflows and inflows associated with a 'project'. Dollar Weighted Average Return is based upon the Internal rate of Return calculation. In other words, it is the discount rate that causes the present value of the future cash flows to be equal to the investment amount.

Extraits

[...] Questions and problems 4. Assume you manage a risk portfolio with an expected return of 15% and a standard deviation of 25%. The T-bill rate is a. Your client chooses to invest 70% of a portfolio in your fund and 30% in T-bills. What is the expected return and standard deviation of the portfolio? rc ) = .30 X 0.70 X 15% = 0.123 or σc = .30 X +.70 X 25% = .175 or per year Investments 5-53 Questions and problems 4. [...]

[...] Historical Returns (cont.) Investments 5-29 Historical Returns (cont.) Investments 5-30 The risk premium is the return demanded by investors for taking on the risk of an investment For a risk-free rate, rf, we can define the risk premium of a portfolio as: Risk premium = E(rp) - rf We will assume the risk-free rate as the return on US Treasury Bills. They are short-term bonds issued by the US Treasury and considered to be default free. Because they are short-term they are also considered to be insensitive to inflation. [...]

[...] The one-year T-bill rate is 5%. Examination of recent returns of the S&P 500 suggest that the standard deviation of returns will be 18%. What does that suggest about the degree of risk aversion of the average investor, assuming that the average portfolio resembles the S&P 500? Investments 5-59 Questions and problems 7. Given the following information: U = – ½ Aσp2 Which investment would you select if you had a risk aversion of And if you were risk aversion were Investments 5-60 Questions and problems 7. [...]

[...] If the risky portfolio is expanded to include all risky assets, then it will reflect the market and systemic risk is reduced. Consider a portfolio of stocks where the number of stocks is increased from 1 to 1,000. The standard deviation of the portfolio will reach an asymptote equal to market standard deviation. Risk in a Portfolio Context (cont.) Investments 5-43 We can show the diversification of risk through another graph that combines the systemic risk of a multi-stock portfolio with the market risk. [...]

[...] What are the investment percentages in the total portfolio? Investments 5-54 Questions and problems 4. Assume you manage a risk portfolio with an expected return of 15% and a standard deviation of 25%. The T-bill rate is c. What is the reward to variability ratio of your portfolio and the client portfolio? Investments 5-55 Questions and problems 4. Assume you manage a risk portfolio with an expected return of 15% and a standard deviation of 25%. The T-bill rate is d. [...]