A commercial bank decides to expand its service menu to include the underwriting of new security offerings (i.e. investment banking) as well as offering traditional lending and deposit services. It discovers that the expected return and risk associated with these two sets of service offerings are

Question

A commercial bank decides to expand its service menu to include the underwriting of new security offerings (i.e. investment banking) as well as offering traditional lending and deposit services. It discovers that the expected return and risk associated with these two sets of service offerings are as follows:

Accepted Answer

Expected return - traditional services 3.5%

Expected return - security underwriting 12%

Standard deviation - traditional services 2.5%

Standard deviation - security underwriting 6%

Correlation of returns between two services +.25

Proportion of revenue - traditional services 65%

Proportion of revenue - security underwriting 35%

Please calculate the effects of the new service on the banking company’s overall return and risk as captured by the bank’s standard deviation of returns.

[latex]E ( R )= W _{ T } R _{ T }+ W _{ S } R _{ S }=.85(10 \%)+.15(15)=10.75 \%[/latex]

[latex] ext { S.D. }=\sqrt{ W _{ T }^{2} * \sigma_{ T }^{2}+ W _{ S }^{2} * \sigma_{ S }^{2}+2} * r_{ TS } * W _{ T } * W _{ S } * \sigma_{ T } * \sigma_{ S }[/latex]

[latex]=\sqrt{.65^{2} * 2.5^{2}+.35^{2} * 6^{2}+2 * .25^{*} .65^{*} .35 * 2.5^{*} 6}[/latex]

=2.96%

Question 14.P.2: A commercial bank decides to expand its service menu to incl...

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