# Geometric Return

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.

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%.

Can anyone explain to me how they got 4.1/4.2?

Cash flow is at beginning of quarter.

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

so for quarter 1

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 0.2 2.4

2.4 / 2.2

For quarter 4

4 3.2 1 4.1

4.1 / (3.2 + 1 ) = 4.1 / 4.2

thankyou very much cpk123

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 = (P1 − P0 + D1)/P0, where P0 is the initial investment, P1 is the price received at the end of the holding period, and D1 is the cash paid by the investment at the end of the holding period.

Can anyone clarify? How are they different?

= 32% (rounded)