Question

if the 12 month continuously compounded return of a security is 9%, its associated 12 month holding period return is closest to: a. 8.62% b. 9.38% c. 9.42%

Answer 1

The 12 month holding period return of a security with a 12 month continuously compounded return of 9% is calculated by transforming the continuously compounded return to a simple interest return. Using the formula A = Pe^rt, the equivalent holding period return is approximately 9.42% after adjusting for the annual compounding. Therefore, the closest answer is 9.42%.

Step-by-step explanation:

The question asks for the 12 month holding period return of a security with a 12 month continuously compounded return of 9%. To calculate this, we need to transform the continuously compounded return to the equivalent simple interest return for the same period. The formula for calculating a continuously compounded return is A = Pert, where A is the future value of the investment, P is the present value, e is the base of natural logarithms (approximately 2.71828), r is the annual interest rate (expressed as a decimal), and t is the time in years. For a 9% rate (or 0.09 as a decimal) over 1 year, this would be:

A = Pe0.09(1)

Calculating this gives:

A = P * e0.09 ≈ P * 1.09417

The holding period return (HPR) would then be approximately 9.42% because we subtract the initial investment (P) from the future value (A) and divide by the initial investment (P), leaving us with an HPR of 1.09417 - 1 = 0.09417, or 9.42% when expressed as a percentage. Hence, the closest answer to the 12 month holding period return of the security is 9.42%.

Answer 2

The associated 12 month holding period return of a security can be calculated using the continuously compounded return formula. The closest 12 month holding period return in this case is 9.39% (option b).

Step-by-step explanation:

The associated 12 month holding period return of a security can be calculated using the continuously compounded return formula. The formula is as follows:

12 month holding period return =
`(e^r - 1) * 100`

where r is the continuously compounded return rate. In this case, the continuously compounded return rate is 9%. Plugging the value into the formula:

12 month holding period return =
`(e^0.09 - 1) * 100`

= 9.39%

Therefore, the closest 12 month holding period return is 9.39% (option b).