Page 324 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 13: Portfolio Performance Evaluation

@ Column (5) - Column (2) Notes
by applying the formula as earlier:
Dollar - Weighted holding Period Return - Annualised

Month/Day Value Days Return Annualised Dollar –Weighted
(1) (2) (3) (4) Returns Annualised
(5) Return
(6)
02/01 1,41,583.26 29 30% 377.58% 78.99%
03/01 1,36,774.79 29 -4.1% -51.60% -10.43%

03/23 96,283.20 23 6.95% 110.290% 15.69%
04/03 1,02,337.94 11 5.25% 174.20% 26.34%
05/01 97,503.60 29 -5.7% -71.74% -10.34%
06/01 1,02,285.92 30 3.9% 47.45% 7.17%

6,76,768.71 107.42%

Time-weighted Return

This time-weighted rate of return is the weighted average of the internal rates of return for the
sub-periods between the cash flows and it is weighted by the length of the sub-periods.
This method considers the market value of the portfolio just before each cash flow occurs.
The percentage change in the value would be 160% as compared with a change in value of 82%,
if there had been no interim cash flow. The time-weighted return of 82% is however more
appropriate return for the fund manager.

Example: Fund A has 10,00,000 under management at time 0. It earns 25% in period 1.
At that time, 5,00,000 is pulled out by other investors. The remaining capital earns negative
10% during period 2. What are the funds time-weighted and rupee-weighted rates of return?
Solution:

The time-weighted rate of return is calculated as a geometric mean of the individual rates of
return. Thus the time-weighted performance is
[(1.25) (0.90)] 0.5 – 1 = 0.0607 = 6.07%

The rupee-weighted rate of return is found as the solution to the internal rate of return problem.
10,00,000 = 5,00,000/(1 + r) + 6,75,000/(1 + r) 2
R = 10.88%

Unit Value Method

When intermediate cash flows are generated, new units can be added to the existing portfolio.
If you assume that the unit value is unchanged while procuring the interim units, the change in
Net Asset Value (NAV) of the portfolio indicates the return on portfolio. In the above illustration,
about 8,000 units are there at a Net Asset Value of 100 at the beginning. Since the value of unit

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