Returns Measures

Question 1

Calculate and explain Holding period return (HPR)

Answer 1

Holding period return (HPR) is simply the percentage increase in the value of an investment over a given time period:

End of period value + dividends revived

/

Beginning of period value

Question 2

Calculate ending value

Answer 2

Initial sum x (period 1 return as integer)

x period 2 return as integer

and so on

Question 3

Define the different return measures:

Gross return

Net return

Pretax nominal return

After tax nominal return

Real return

Leveraged return

Answer 3

Gross return refers to the total return on a security portfolio before deducting fees for the management and administration of the investment account.

Net return refers to the return after these fees have been deducted. Note that commissions on trades and other costs that are necessary to generate the investment returns are deducted in both gross and net return measures.

Pretax nominal return refers to the return prior to paying taxes. Dividend income, interest income, short-term capital gains, and long-term capital gains may all be taxed at different rates.

After-tax nominal return refers to the return after the tax liability is deducted.

Real return is nominal return adjusted for inflation. Consider an investor who earns a nominal return of 7% over a year when inflation is 2%. The investor’s approximate real return is simply 7 − 2 = 5%. The investor’s exact real return is slightly lower, 1.07 / 1.02 − 1 = 0.049 = 4.9%.

A leveraged return refers to a return to an investor that is a multiple of the return on the underlying asset. The leveraged return is calculated as the gain or loss on the investment as a percentage of an investor’s cash investment. An investment in a derivative security, such as a futures contract, produces a leveraged return because the cash deposited is only a fraction of the value of the assets underlying the futures contract. Leveraged investments in real estate are very common: investors pay only a portion of a property’s cost in cash and borrow the rest.

Question 4

Calculating money-weighted return with the TI Business Analyst II Plus

Assume an investor buys a share of stock for $100 at t = 0 and at the end of the year (t = 1), she buys an additional share for $120. At the end of Year 2, the investor sells both shares for $130 each. At the end of each year in the holding period, the stock paid a $2.00 per share dividend. What is the money-weighted rate of return?

Answer 4

Key Strokes Explanation Display
[CF] [2nd][CLR WORK] Clear Cash Flow Registers CF0 = 0.00000
100 [ENTER] Initial Cash Outlay CF0 = +100.00000
[↓] 118 [ENTER] Period 1 Cash Flow C01 = +118.00000
[↓] [↓] 264 [+/–] [ENTER] Period 2 Cash Flow C02 = –264.00000
[IRR] [CPT] Calculate IRR IRR = 13.86122