Question

You own a portfolio that has 6,600 shares of stock A, which is priced at 18 dollars per share and has an expected return of 7.42 percent, and 3,300 shares of stock B, which is priced at 20.2 dollars per share and has an expected return of 11.15 percent. The risk-free return is 3.57 percent and inflation is expected to be 1.94 percent. What is the expected real return for your portfolio? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Rogelio’s portfolio is worth 66,700 dollars and has three stocks. It has 16,100 dollars of stock A, which has an expected return of 2.4 percent; it has 2,200 shares of stock B, which has a share price of 5.5 dollars and an expected return of 10.61 percent; and it has some stock C, which has an expected return of 15.41 percent. What is the expected return of Rogelio’s portfolio? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

First problem:

Expected return on portfolio (Nominal Rate, Rp)= Wa*Ra + Wb*Rb

Where Wa= Weight of stock A, Ra= Return on stock A, Wb= Weight of stock B and Rb=return on stock B.

Number of shares of A= 6,600 and price of A= $18. Therefore, value of stock A= 6600*18= $118,800

Number of shares of B= 3,300 and price of B= $20.2 Therefore, value of stock B= 3300*20.2= $66,660

Weight of Stock A (Wa)= 118800/(118800+66660) = 0.6406

Weight of Stock B (Wb)= 66660/(118800+66660) = 0.3594

Given, Ra= 7.42% and Rb= 11.15%

Substituting these values, Expected Return of portfolio (Nominal Rate)

= 0.6406*0.0742 + 0.3594*0.1115 = 0.0876

Also given that inflation = 1.94%

Real Rate of Return= (Nominal Rate- Inflation)/(1+Inflation)

Therefore, real rate of return= (0.0876-0.0194)/(1+0.0194) = 0.0669

Second problem:

Expected return on portfolio (Nominal Rate, Rp)= Wa*Ra + Wb*Rb + Wc*Rc

Where Wa= Weight of stock A, Ra= Return on stock A, Wb= Weight of stock B, Rb=turn on stock B, Wc= Weight of Stock C and Rc= Return on Stock C.

Given,

Value of stock A= $16,100

Number of shares of B= 2200 and price ofBA= $5.5 Therefore, value of stock B= 2200*5.5 = $12,100

Total portfolio value= $$66,700.

Therefore, value of stock B= 66700-(16100+12100)= $38,500

Weight of Stock A (Wa)= 16100/66700= 0.241379

Weight of Stock B (Wb)= 12100/66700 = 0.181409

Weight of Stock C (Wc)= 38500/66700 = 0.577211

Given, Ra= 2.4%, Rb= 10.61% and Rc= 15.41%

Substituting these values, Expected Return of portfolio= 0.241379*2.4% + 0.181409*10.61% +0.577211*15.41%

= 0.005793 + 0.019248 + 0.088948 = 0.113989