FM for Actuaries

Rates of Return 133
measure of the rate of return of the project and takes account of the time
value of money.
2. The internal rate of return usually cannot be calculated analytically, and its
computation requires numerical methods. Although simple projects have
unique internal rate of return, more complicated projects may have multiple
solutions of internal rate of return.
3. The 1-period rate of return of a fund can be computed using the time-weighted
rate of return or the dollar-weighted rate of return. The time-weighted rate of
return requires data for the cash flows as well as the value of the fund at the
time of cash flows. The dollar-weighted rate of return does not require the
fund value to be marked to market.
4. Multiple-period return of a fund can be measured using the geometric mean
rate of return or the arithmetic mean rate of return. The geometric mean
rate of return measures the fund’s performance over the period based on the
buy-and-hold assumption. The arithmetic mean rate of return measures the
average return of the fund in a random year over the period.
5. The time-weighted and dollar-weighted methods can be used to measure the
return of a fund over an extended period, if the data about of the cash flows
over the period are available.
6. The rate of return of a portfolio is equal to the weighted average of the rates of
return of its component assets. Portfolio diversification may lead to reduction
in standard deviation over individual assets in the portfolio.
7. Short sale is the sale of a security that the seller does not own. Short selling
involves the creation of a margin account, and the return of the short-sale
strategy should be based on the margin deposits.
8. Investment-year method and portfolio method are two methods of crediting
interests to investors of a fund. The purpose is to have a more equitable
method of crediting interests with respect to the different timings of the investments.
9. The net present value rule accepts projects with positive net present value
discounted at the required rate of return. This method can be extended to
allow the required rate of return to vary with the horizons of the cash flows.
The IRR and DPP methods are two alternative methods of project appraisal.