Question

Your portfolio consists of 120 shares of CSH and 45 shares of​ EJH, which you just bought at $21 and $32 per​ share, respectively.

a. What fraction of your portfolio is invested in​ CSH? In​ EJH?

b. If CSH increases to $25 and EJH decreases to $27​, what is the return on your​ portfolio?

Answer 1

(a) Value of CSH shares = 120 * $21 = $2520

Value of EJH shares = 45 * $32 = $1440

Total value of portfolio = $2520 + $1440 = $3960

Now, we will calculate fraction invested in each share by the following formula:

Fraction invested = Value of stock or share / Total value of portfolio

Fraction invested in CSH = $2520 / $3960 = 0.64 or 64%

Fraction invested in EJH = $1440 / $3960 = 0.36 or 36%

(b) First we will caluculate return on both the shares by the following formula:

Return = New share price - Old share price / Old share price

Return on CSH shares = $25 - $21 / $21 = $4 / $21 = 0.19 or 19%

Return on EJH shares = $27 - $32 / $32 = - $5 / $32 = - 0.16 or -16%

Now, we will calculate expected return of the portfolio as below:

Expected return = w1 * r1 + w2* r2

where, w1 = Fraction invested in CSH = 64%

w2 = Fraction invested in EJH = 36%

r1 = Return on CSH shares = 19%

r2  = Return on EJH shares = -16%

Now, putting these values in the expected return formula, we get,

Expected return = ((64% * 19%) + (36% * -16%))

Expected return = 12.16% - 5.76% = 6.4%