Question

Investments An investor has up to $$\$ 250,000$$ to invest in two types of investments. Type A investments pay \(7 \%\) annually and type \(\mathrm{B}\) pay \(12 \%\) annually. To have a well-balanced portfolio, the investor imposes the following conditions. At least one-fourth of the total portfolio is to be allocated to type A investments and at least one-fourth is to be allocated to type \(\mathrm{B}\) investments. What is the optimal amount that should be invested in each type of investment? What is the optimal return?

Short answer

The optimal amounts to invest are $62,500 in type A investments and $187,500 in type B investments, resulting in an optimal annual return of $26,875.

Step-by-step solution

Understand the Constraints

Before we can determine the optimal investment strategy, we must understand the constraints. The investor must invest at least one-fourth of their total portfolio in both Type A and Type B investments. As the total investment portfolio is $250,000, this means the investor must invest at least $62,500 in both Type A and Type B investments. This means the combined minimum investment in Type A and B is $125,000, leaving the investor $125,000 remaining to allocate as they see fit.

Calculate Optimal Investment

To maximize the return, the remaining $125,000 should be invested in the option with the higher return rate, which is Type B investment at 12%. Therefore, the optimal amount to invest in Type A and Type B investments is $62,500 and $187,500 respectively.

Calculate Optimal Return

The return from an investment can be calculated by multiplying the amount invested with the annual rate. Therefore, the optimal return can be calculated by summing up the returns from both investments. From Type A, the return is \(62,500 * 0.07 = 4,375\) USD and from Type B, the return is \(187,500 * 0.12 = 22,500\) USD. So, the optimal return is \(4,375 + 22,500 = 26,875\) USD.

Key concepts

Portfolio Allocation

When crafting an investment strategy, one of the most critical decisions is portfolio allocation. This concept involves deciding how to distribute your investments among various asset classes, such as stocks, bonds, or, as seen in our exercise, different types of investment opportunities with varying rates of return. Effective portfolio allocation balances the investor's risk preferences with their return objectives and takes into account the investment horizon as well as financial goals.

For instance, the investor in our exercise elected to allocate funds between two types of investments, ensuring that at least one-fourth is dedicated to each. This can be framed as a form of diversification, aiming to manage risk by not overcommitting to a single asset. Diversifying your investments can help reduce the impact of poor performance from a single investment on the overall portfolio.

Rate of Return

The rate of return is a crucial measure for assessing the performance of an investment. It is expressed as a percentage and represents the gain or loss on an investment over a specified period, relative to the original amount of investment. As we can see in our textbook exercise, Type A investments yield a 7% return, while Type B investments offer a 12% return.

To calculate the rate of return, one can use the formula: \[ \text{Rate of Return} = \frac{\text{Total Return}}{\text{Original Investment}} \times 100\]. Investing in assets with higher returns can potentially increase your income over time, but it's also important to consider the associated risks. Generally, investments with higher rates of return are riskier.

Investment Constraints

Investors often face investment constraints, which are restrictions on how they can allocate their funds. These constraints can stem from a variety of sources such as regulatory requirements, liquidity needs, tax considerations, or personal risk tolerance. In our exercise, the investor's constraints dictate a minimum investment in both Type A and B investments.

These constraints are critical to follow when building an investment strategy as they directly influence potential outcomes and ensure that certain goals or requirements are met. Constraints can also help protect the investor from making overly risky moves or becoming too heavily weighted in a particular asset or sector. When giving investment advice, it's important always to consider any constraints the investor might have.

Maximizing Investment Return

Investors typically seek to maximize their return within their risk tolerance and given constraints. In the exercise, this goal is achieved by allocating the remaining funds after meeting the minimum required investment into the option with the greater rate of return. This strategy leverages the ability to earn more from investments with higher yield, thus increasing the overall portfolio performance.

However, maximizing returns isn't just about chasing the highest rates; it involves a careful assessment of potential rewards against the risks. It's also about maintaining an optimal balance that aligns with your long-term financial goals. Being strategic about how and where to invest surplus funds, as demonstrated by the investor in our scenario, is vital for achieving an optimal balance between growing wealth and managing investment risks.