A bank is considering adding life insurance underwriting to the services it offers.It has estimated that the expected return and standard deviation of its traditional services are 12 percent and 6 percent respectively.It has also estimated that the expected return and standard deviation of its new underwriting services are 18 percent and 10 percent respectively.The correlation between these services has been estimated to be +0.10 and the bank estimates that 90 percent of its business will be from traditional services and 10 percent from the new underwriting services.What is the expected standard deviation of the new combination of services?

Question

Quizplus · Accepted Answer

To find the expected standard deviation of the new combination of services, we need to use the formula:

σ_comb = √[w_trad^2*σ_trad^2 + w_under^2*σ_under^2 + 2*w_trad*w_under*ρ*σ_trad*σ_under]

where

w_trad = 0.9 (weight of traditional services)
w_under = 0.1 (weight of underwriting services)
σ_trad = 0.06 (standard deviation of traditional services)
σ_under = 0.10 (standard deviation of underwriting services)
ρ = 0.10 (correlation between services)

Substituting these values, we get:

σ_comb = √[0.9^2*0.06^2 + 0.1^2*0.10^2 + 2*0.9*0.1*0.10*0.06*0.10]

σ_comb = 0.0559 or 5.59%

Therefore, the expected standard deviation of the new combination of services is 5.59%, which is closest to option C (5.59%).

A Bank Is Considering Adding Life Insurance Underwriting to the Services