An analyst gathers the following information ($ millions) about the performance of a portfolio:

Quarter

Value at Beginning

of Quarter

(prior to inflow or outflow)

Cash Inflow (Outflow)

At Beginning of Quarter

Value at End

of Quarter

1

2.0

0.2

2.4

2

2.4

0.4

2.6

3

2.6

(0.2)

3.2

4

3.2

1.0

4.1

The portfolio’s annual time-weighted rate of return (%) is closest to:

A. 8.

B. 27.

C. 32.

Answer: C

In this case, the quarterly holding periods are 2.4/2.2 = 1.0909, 2.6/2.8 = 0.9286, 3.2/2.4 = 1.3333, and 4.1/4.2 = 0.9762. The time-weighted return is thus (1.0909 × 0.9286 × 1.3333 × 0.9762) - 1 = 1.3185 – 1 = 0.3185 or 31.85%.

Was just confused between these 2 interpretations of the formula,

HPR for each quarter = Value at End / (Value at beginning + Cash Flow in quarter)

the fundamental concept of holding period return (HPR), the return that an investor earns over a specified holding period. For an investment that makes one cash payment at the end of the holding period,

HPR = (P_{1} − P_{0} + D_{1})/P_{0}, where P_{0} is the initial investment, P_{1} is the price received at the end of the holding period, and D_{1} is the cash paid by the investment at the end of the holding period.