An investment portfolio consists of three asset classes: Equities, Bonds, and Real Estate.… — GMAT

An investment portfolio consists of three asset classes: Equities, Bonds, and Real Estate. The total monetary value of Equities to Bonds is in the ratio $3 : 2$ , and the total value of Bonds to Real Estate is in the ratio $4 : 5$ . Over the past year, Equities yielded an average return of $12\%$ . If the overall weighted average return of the entire portfolio was $10.4\%$ , and the average percentage return of Bonds was $25\%$ higher than the average percentage return of Real Estate, what was the average percentage return of Bonds?

Answer: 10.5 %

Answer

The average percentage return of Bonds was 10.5%.

The correct return of Bonds is obtained by first unifying the given ratios into a continuous ratio of weights

6 : 4 : 5

for Equities, Bonds, and Real Estate respectively. Substituting these weights and the algebraic relation between Real Estate return (

r

) and Bond return (

1.25r

) into the weighted average expression yields

r = 8.4\%

. Multiplying this by

1.25

gives the bond return of

10.5\%

Step-by-Step Solution

Determine the combined ratio of portfolio weights for all three asset classes

The ratio Equities : Bonds : Real Estate is 6 : 4 : 5, giving a total weight sum of 15 units.

Since Equities to Bonds is 3:2 (or 6:4) and Bonds to Real Estate is 4:5, the common term Bonds allows combining the ratios into 6 : 4 : 5.

Express the unknown asset returns in terms of a single variable

Return of Real Estate =

r\%

, Return of Bonds =

1.25r\%

The problem states the return of Bonds is 25% higher than that of Real Estate (

r + 0.25r = 1.25r

Set up and solve the weighted average formula for the portfolio

r = 8.4\%

Using

\frac{6(12) + 4(1.25r) + 5r}{15} = 10.4

, we get

72 + 10r = 156

, leading to

10r = 84

Calculate the targeted return for Bonds

Return of Bonds =

10.5\%

Multiplying

1.25

8.4

yields

10.5

Key Concept

Combining multiple ratios to establish weighted average component weights and solving multi-variable weighted average equations

Estimated Time:2m 30s

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