An financial analyst is in the process of measuring the annualized return of an investment portfolio. Consider the following information: t0: purchase an initial 1 share of Microscam for $65.40 t1: purchase an additional 1 share of Microscam for $68.12 t1: receive a dividend of $0.75 t2: purchase an additional 1 share of Microscam for $75.95 t2: receive a dividend of $0.77 t3: sell 3 shares for $82.76 per share
Assuming no taxes or transaction costs, that dividends are not reinvested, and that each period represents one year, what is the time-weighted rate of return per year on this portfolio?
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A. B. C. D. E. F.F
The time-weighted rate of return is the preferred method of return calculation in the investment management industry, primarily because the return calculation it produces is not sensitive to significant additions and withdrawals of funds from portfolios under examination. The calculation of the time-weighted rate of return involves three steps, which are illustrated as follows:
Step 1:
Price the portfolio immediately prior to any significant additions or withdrawals. Separate the portfolio into a series of subperiods based on the dates of cash inflows and outflows.
Step 2:
Calculate the holding period return for each subperiod.
Step 3:
Determine the annualized holding period return by linking or compounding the holding period return of each subperiod. If the investment is for more than one year, use the geometric mean of the annual returns as the time-weighted rate of return. If the investment is for less than one year, compound the subperiod returns to obtain an annualized measurement.
To begin the process of determining the time-weighted rate of return, we would break the portfolio up into the following series of cash flows. However, in this example, the cash flows are already aggregated for us and we can move on to the next step: determining the holding period return for each subperiod. This process is detailed as follows: t1: [($68.12 ending price + $0.75 dividend received - $65.40 beginning price) / $65.40 beginning price] = 5.306%. t2: [($75.95 ending price + $0.77 dividend received - $68.12 beginning price) / $68.12 ending price] = 12.625% t3: [$82.76 ending price - $75.95 beginning price / $75.95 beginning price] = 8.966%
Now that the holding period returns for each subperiod have been calculated, the determination of the time-weighted rate of return can take place. Since the duration of these transactions exceeds one year,we must take the geometric mean of the annual returns to obtain the time-weighted rate of return. This is done by taking the cube root of [(1 + .05306) * (1 + .12625) * (1 + .08966], subtracting 1, and multiplying by 100%, which leads to a time-weighted rate of return of .0892 or
8.92%.
If you chose 10.73%, remember that it is the geometric mean that is used in the time-weighted rate of return calculation, not the arithmetic mean.