Question

You have been asked for your advice in selecting a portfolio of assets and have been supplied with the following​ data:. You have been told that you can create two portfolios—one consisting of assets A and B and the other consisting of assets A and C—by investing equal proportions ​(50%​) in each of the two component assets.

f. What would happen if you constructed a portfolio consisting of assets​ A, B, and​ C, equally​ weighted? Would this reduce risk or enhance​ return?

If you constructed a portfolio consisting of assets​ A, B, and​ C, equally​ weighted, the average expected​ return,

rp​, for Portfolio ABC is ___ ​(Round to one decimal​place.)

Projected Return

year	asset a	asset b	asset c
2018	13%	17%	13%
2019	15%	15%	15%
2020	17%	13%	17%

Answer 1

The portfolio can consist of assets A, B & C. To calculate the portfolio return, we will use the yearly returns of 2018, 2019 & 2020 as well as the average return of all years.

Calculation of Average Returns:

Average Return = Sum of Returns / No. of Returns

Asset A = (13 + 15 + 17) / 3 = 15%

Asset B = (17 + 15 + 13) / 3 = 15%

Asset C = (13 + 15 + 17) / 3 = 15%

Choice of Portfolio:

1. Portfolio 1 - Asset A & B (equal proportion)
2. Portfolio 2 - Asset A & C (equal proportion)

Portfolio Return (R_P) = where R_i = Return of Asset i

w_i = Proportion/ weight of Asset i

Calculation of Portfolio Return (R_P):

Portfolio 1 - Asset A & B

For 2018 = 13% * 0.5 + 17% * 0.5 = 15%

For 2019 = 15% * 0.5 + 15% * 0.5 = 15%

For 2020 = 17% * 0.5 + 13% * 0.5 = 15%

Average = 15% * 0.5 + 15% * 0.5 = 15%

Conclusion: The portfolio return is constant at 15% because the assets are perfectly negatively corelated (Correlation coefficient = -1). % increase in return of one asset is equal to % decrease in return of another asset. As the proportion of asset is equal, the portfolio risk (variance) will be 0 (Nil).

Portfolio 2 - Asset A & C

For 2018 = 13% * 0.5 + 13% * 0.5 = 13%

For 2019 = 15% * 0.5 + 15% * 0.5 = 15%

For 2020 = 17% * 0.5 + 17% * 0.5 = 17%

Average = 15% * 0.5 + 15% * 0.5 = 15%

Conclusion: The portfolio return is equal to the individual asset returns because the assets are perfectly positively corelated (Correlation coefficient = +1). % increase in return of one asset is equal to % increase in return of another asset. As the proportion of asset is equal, the portfolio risk (variance) will be the weighted average of asset variances.

Portfolio 3 - Asset A, B & C in equal proportion

If we create portfolio 3, it would reduce risk when compared to portfolio 2 at average level. However, the portfolio return will be constant at 15%.

Average Return = 15% * ¹/₃ + 15% * ¹/₃ + 15% * ¹/₃ = 15%

However, the yearly returns will differ from portfolio 1 & 2

For 2018 = 13% * ¹/₃ + 17% * ¹/₃ + 13% * ¹/₃ = 14.3%

For 2019 = 15% * ¹/₃ + 15% * ¹/₃ + 15% * ¹/₃ = 15%

For 2020 = 17% * ¹/₃ + 13% * ¹/₃ + 17% * ¹/₃ = 15.7%

Conclusion: If the investor prefers a diversified portfolio, s/he should invest in Portfolio 3. If the investor prefers a riskless investment, s/he should prefer Portfolio 1. If the market is bullish, prefer Portfolio 1 for higher returns.