Question

Penny Francis inherited a​ $200,000 portfolio of investments from her grandparents when she turned 21 years of age. The portfolio is comprised of Treasury bills and stock in Ford​ (F) and Harley Davidson​ (HOG):

a. Based on the current portfolio composition and the expected rates of​ return, what is the expected rate of return for​ Penny's portfolio?

b. If Penny wants to increase her expected portfolio rate of​ return, she can increase the allocated weight of the portfolio she has invested in stock​ (Ford and Harley​ Davidson) and decrease her holdings of Treasury bills. If Penny moves all her money out of Treasury bills and splits it evenly between the two​ stocks, what will be her expected rate of​ return?

c. If Penny does move money out of Treasury bills and into the two​ stocks, she will reap a higher expected portfolio​ return, so why would anyone want to hold Treasury bills in their​ portfolio?

	Expected Return	$ Value
TREASURY BILLS	4.4%	68,000
FORD (F)	7.4%	68,000
HARLEY DAVIDSON (HOG)	13.7%	56,000

Answer 1

21. a) We would first need to allocate weights, on further inspection the total $ value of the portfolio is 192,000

Weight of T Blls = 68000/192000 = 0.354

Weight of Ford = 68000/192000 = 0.354

Weight of Harley Davidson = 56000/192000 = 0.292

Current Expected Rate of Return = 4.4% * 0.354 + 7.4% * 0.354 + 13.7% * 0.292 = 8.18%

b) New dollar amounts for Ford and Harley

Ford = 68000 + 0.5*68000 = 102,000

Harley = 56000 + 0.5*68000 = 90000

New weights -

Ford = 102000/192000 = 0.531

Harley = 90000/192000 = 0.469

Expected Rate of Return = 7.4% * 0.531 + 13.7% * 0.469 = 10.35%

c) Stocks are risky assets. Their returns can be pretty volatile. T Bills on the other hand are considered to be virtually risk free. Adding T Bills diversifies your portfolio and reduces the total risk you face which results in a form of protection from adverse moment. For example currently stock prices are declining so you would experience negative returns on your investment but in the case of T Bill which has a fixed return rate and thus would result in interest and principal payments regardless if the economy is performing well or not. Thus, adding more stability to your returns.