Data table

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**Expected Return**

​ $ **Value** 

 Treasury bills
  
4.54.5​%

290 comma 000290,000

​ S&P 500 Index Fund
  
8.88.8​%

437 comma 000437,000

 Emerging Market Fund

12.212.2​%

273 comma 000​(Computing **the portfolio expected rate of**​ return) 

Bronc GersonBronc Gerson 

is 60 years of age and is considering retirement. 

BroncBronc 

got his name from the fact that as a young man he spent several years in the rodeo circuit competing as a bareback riderat. His retirement portfolio currently is valued at 

​$1 comma 000 comma 0001,000,000 

and is allocated in Treasury​ bills, an​ S&P 500 Index​ fund, and an emerging market fund as​ follows: 

LOADING...

.

**a.** Based on the current portfolio composition and the expected rates of return given​ above, what is the expected rate of return for 

Bronc'sBronc's 

​portfolio?

**b.** 

BroncBronc 

is considering a reallocation of his investments to include more Treasury bills and less exposure to emerging markets. If 

BroncBronc 

moves all of his money from the emerging market fund and puts it in Treasury​ bills, what will be the expected rate of return on the resulting​ portfolio?

​(*Hint*​: 

Use at least four decimal places in all​ calculations.)

Question content area bottom

Part 1

**a.** Based on the current portfolio composition and the given expected rates of​ return, the expected rate of return for 

Bronc'sBronc's 

portfolio is 

enter your response here​%. 

 ​(Round to two decimal​ places.)

To calculate the expected rate of return for Bronc Gerson's portfolio, we need to use the formula for the expected return based on the weights of each investment and their respective expected returns.

### Current Portfolio Composition:
- **Treasury Bills**: $290,000 with an expected return of 4.5%
- **S&P 500 Index Fund**: $437,000 with an expected return of 8.8%
- **Emerging Market Fund**: $273,000 with an expected return of 12.2%

### Total Portfolio Value:
\[
\text{Total Portfolio Value} = 290,000 + 437,000 + 273,000 = 1,000,000
\]

### Expected Return Calculation:
The expected return $ E(R) $ is calculated as:
\[
E(R) = \left( \frac{V_1}{V_T} \times R_1 \right) + \left( \frac{V_2}{V_T} \times R_2 \right) + \left( \frac{V_3}{V_T} \times R_3 \right)
\]
Where:
- $ V_1, V_2, V_3 $ are the values of the investments
- $ V_T $ is the total portfolio value
- $ R_1, R_2, R_3 $ are the expected returns for each investment

Plugging in the values:
\[
E(R) = \left( \frac{290,000}{1,000,000} \times 0.045 \right) + \left( \frac{437,000}{1,000,000} \times 0.088 \right) + \left( \frac{273,000}{1,000,000} \times 0.122 \right)
\]

Calculating each term:
1. **Treasury Bills**:
\[
\frac{290,000}{1,000,000} \times 0.045 = 0.01305
\]
2. **S&P 500 Index Fund**:
\[
\frac{437,000}{1,000,000} \times 0.088 = 0.038536
\]
3. **Emerging Market Fund**:
\[
\frac{273,000}{1,000,000} \times 0.122 = 0.033366
\]

Now, summing these results:
\[
E(R) = 0.01305 + 0.038536 + 0.033366 = 0.085952
\]

### Final Expected Rate of Return:
\[
E(R) \approx 0.085952 \times 100 \approx 8.60\%
\]

Thus, the expected rate of return for Bronc's portfolio is approximately **8.60%** (rounded to two decimal places).

---

### Part (b):
If Bronc moves all of his money from the Emerging Market Fund into Treasury Bills, the new portfolio composition will be:
- **Treasury Bills**: $290,000 + $273,000 = $563,000
- **S&P 500 Index Fund**: $437,000
- **Emerging Market Fund**: $0

**New Total Portfolio Value**: $1,000,000

### New Expected Return Calculation:
\[
E(R) = \left( \frac{563,000}{1,000,000} \times 0.045 \right) + \left( \frac{437,000}{1,000,000} \times 0.088 \right) + \left( \frac{0}{1,000,000} \times 0.122 \right)
\]

Calculating each term:
1. **Treasury Bills**:
\[
\frac{563,000}{1,000,000} \times 0.045 = 0.025335
\]
2. **S&P 500 Index Fund**:
\[
\frac{437,000}{1,000,000} \times 0.088 = 0.038536
\]
3. **Emerging Market Fund**:
\[
0 = 0
\]

Summing these results:
\[
E(R) = 0.025335 + 0.038536 + 0 = 0.063871
\]

### Final New Expected Rate of Return:
\[
E(R) \approx 0.063871 \times 100 \approx 6.39\%
\]

So, the expected rate of return on the resulting portfolio will be approximately **6.39%**.

---

Would you like more details or do you have any questions? Here are some related questions to consider:

1. How does changing the allocation affect risk?
2. What are the implications of a lower expected return?
3. What are the benefits of investing in emerging markets?
4. How can Bronc balance risk and return in his portfolio?
5. What factors should Bronc consider before reallocating his investments?

**Tip:** Always consider your risk tolerance when reallocating investments, especially close to retirement.

Based on the current portfolio composition and the expected rates of return given above, what is the expected rate of return for Bronc's portfolio?

Discover how to calculate the expected rate of return for Bronc Gerson's investment portfolio, which includes Treasury bills, an S&P 500 Index fund, and an Emerging Market Fund. Learn the formulas and concepts behind portfolio expected returns.

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