What is the standard deviation of returns on a well-diversified portfolio with a beta of 1.25 if the standard deviation of the market portfolio equals 18%?

the standard deviation of the portfolio is σP = 22.5%

Step-by-step explanation:

since the variance of the portfolio σP² is

σP² = β²*σM²+σ²(e)

where

β= Portfolio's beta

σM = standard deviation of the market portfolio

σ²(e) = variance of the unexpected returns of the portfolio ( diversifiable risk)

for a well-diversified portfolio σ²(e) = 0, then

σP² = β²*σM²

σP=β*σM

replacing values

σP = β*σM = 1.25*0.18 = 0.225 = 22.5%

σP = 22.5%

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for