ramesh wanted to invest an amount for a week he also wanted to guarantee maximum returns on his investment he was considering three alternatives for this investment he can utilize each of these completely or partially along with the others the alternatives are given below alternative 1 invest in the mutual funds of x ltd. if a rise occurs in the tock market he would get 8 percent return if a fall occurs in it he would get -5 percent returns. alternative 2 invest in the mutual funds of y ltd if a rise occurs in the stock market he would get -4 percent retun. if a fall occurs in it he would get 3 percent return. alternative 3 invest in a bank which assures 0.15 percent return. find the greatest assured return to ramesh (a) 0.2 percent (b) 0.15 percent (c) 0.25 percent (d) 0.3 percent .find the stratergy which will maximise the assured return to ramesh (a) equal investment in each altenative. (b) 35 percent in alternative 1 and 65 percent in alternative 2. (c) 40 percent in alternative 1 and 60 percent in alternative 2. (d) 60 percent in alternative 1 and 40 percent in alternative 2.

To solve this problem, we need to determine the investment strategy that guarantees the highest return for Ramesh regardless of the stock market's behavior (whether it rises or falls). We'll consider each alternative and the possible investment combinations.

### Returns for each alternative:
1. **Alternative 1** (X Ltd. Mutual Funds):
   - Rise in stock market: +8%
   - Fall in stock market: -5%

2. **Alternative 2** (Y Ltd. Mutual Funds):
   - Rise in stock market: -4%
   - Fall in stock market: +3%

3. **Alternative 3** (Bank):
   - Guaranteed return: +0.15%

### Given Strategies:
- **(a)** Equal investment in each alternative.
- **(b)** 35% in Alternative 1 and 65% in Alternative 2.
- **(c)** 40% in Alternative 1 and 60% in Alternative 2.
- **(d)** 60% in Alternative 1 and 40% in Alternative 2.

### Step 1: Calculate the guaranteed return for each strategy.

#### **Strategy (a): Equal investment in each alternative**
- Let's assume Ramesh invests \( \frac{1}{3} \) in each alternative.
- Return during a market rise: 
  \[
  \text{Return} = \frac{1}{3} \times 8\% + \frac{1}{3} \times (-4\%) + \frac{1}{3} \times 0.15\% 
  \]
  \[
  \text{Return} = \frac{8 - 4 + 0.15}{3} = \frac{4.15}{3} \approx 1.38\%
  \]
- Return during a market fall:
  \[
  \text{Return} = \frac{1}{3} \times (-5\%) + \frac{1}{3} \times 3\% + \frac{1}{3} \times 0.15\%
  \]
  \[
  \text{Return} = \frac{-5 + 3 + 0.15}{3} = \frac{-1.85}{3} \approx -0.62\%
  \]

This strategy does not guarantee a positive return because it could result in a negative return in case of a market fall.

#### **Strategy (b): 35% in Alternative 1 and 65% in Alternative 2**
- Return during a market rise:
  \[
  \text{Return} = 0.35 \times 8\% + 0.65 \times (-4\%)
  \]
  \[
  \text{Return} = 2.8\% - 2.6\% = 0.2\%
  \]
- Return during a market fall:
  \[
  \text{Return} = 0.35 \times (-5\%) + 0.65 \times 3\%
  \]
  \[
  \text{Return} = -1.75\% + 1.95\% = 0.2\%
  \]

This strategy guarantees a return of 0.2% regardless of the market condition.

#### **Strategy (c): 40% in Alternative 1 and 60% in Alternative 2**
- Return during a market rise:
  \[
  \text{Return} = 0.4 \times 8\% + 0.6 \times (-4\%)
  \]
  \[
  \text{Return} = 3.2\% - 2.4\% = 0.8\%
  \]
- Return during a market fall:
  \[
  \text{Return} = 0.4 \times (-5\%) + 0.6 \times 3\%
  \]
  \[
  \text{Return} = -2\% + 1.8\% = -0.2\%
  \]

This strategy does not guarantee a positive return in case of a market fall.

#### **Strategy (d): 60% in Alternative 1 and 40% in Alternative 2**
- Return during a market rise:
  \[
  \text{Return} = 0.6 \times 8\% + 0.4 \times (-4\%)
  \]
  \[
  \text{Return} = 4.8\% - 1.6\% = 3.2\%
  \]
- Return during a market fall:
  \[
  \text{Return} = 0.6 \times (-5\%) + 0.4 \times 3\%
  \]
  \[
  \text{Return} = -3\% + 1.2\% = -1.8\%
  \]

This strategy does not guarantee a positive return in case of a market fall.

### Step 2: Compare with the Bank (Alternative 3)
- Alternative 3 guarantees a return of 0.15%.

### Conclusion:
- The highest guaranteed return is 0.2%, which is obtained by using **Strategy (b): 35% in Alternative 1 and 65% in Alternative 2**.
- Therefore, the answer is:
  - **(a) 0.2 percent**
  - **(b) 35 percent in alternative 1 and 65 percent in alternative 2**.

Would you like more details or have any questions? 

Here are some related questions:
1. What would happen if the investment proportions were slightly adjusted?
2. How would Ramesh's strategy change if the bank's guaranteed return increased?
3. What if the return percentages for the mutual funds were different?
4. How does risk play a role in determining the investment strategy?
5. What would be the impact of inflation on the investment returns?

**Tip:** Always evaluate the worst-case scenario when dealing with investments to ensure that your strategy is robust.

Discover how to maximize investment returns for Ramesh by strategically allocating funds across three investment alternatives. Analyze different investment strategies to ensure maximum guaranteed returns regardless of market fluctuations. Learn about investment in mutual funds and bank options with specific return rates.

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