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Statistícs for lnvesting. A mutual funds compamy's nevrsletter says "A well. diversified port folio includes assets with low correlations." The newsletter includes a table of correlations bet ween the returns on various classes of investments. For example, the correlatjon between municipal honds and largecap stoclss is \(0.50\), and the correlation hetween municipal bonds and small cap stocks is \(0.21\). a. Pachel imvests heavily in municipal bonds. She wants to diversify by adding an investment whase returns do not closely follow the returns on her bonds. Should she choose largecap stocks ar small-cap stocks for this purpose? Explain your answer. b. If Rachel wants an invest meat that tends to increase when the return on her honds drops, what kind of correlation should she look for?

Step by step solution

01

Understanding the Problem

We need to help Rachel choose between large-cap stocks and small-cap stocks to diversify her investment in municipal bonds. Diversification is desirable with assets having low or negative correlation. Additionally, if Rachel wants an investment that increases when municipal bonds' returns decrease, she should look for a negative correlation.

02

Analyze Correlations for Diversification

To diversify Rachel's investments, we should compare correlations of large-cap stocks and small-cap stocks with municipal bonds. Municipal bonds have a correlation of 0.50 with large-cap stocks and 0.21 with small-cap stocks. Lower correlation indicates less synchronized movement, which is better for diversification.

03

Select for Diversification

Between the two options, small-cap stocks have a lower correlation (0.21) with municipal bonds compared to large-cap stocks (0.50). Therefore, small-cap stocks would be the better choice for diversification purposes as they offer less synchronized returns with municipal bonds.

04

Identify the Desired Correlation for Opposite Movement

For an investment that tends to increase when municipal bonds decrease (opposite movement), Rachel should look for an investment with a negative correlation with municipal bonds. Negative correlation means that when one investment goes down, the other tends to go up.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Diversified Portfolio

Investing involves allocating money across various asset classes to achieve the best possible returns with a manageable amount of risk. A diversified portfolio is key to this approach. It includes a mix of different types of investments, such as stocks, bonds, and other assets, which often have different levels of risk and return.

Diversification helps to spread risk because not all asset types will react to market changes in the same way.

• Spreads risk by investing in a variety of assets.
• Aims to balance potential returns against the likelihood of risks.
• Seeks to minimize the impact of any one asset's poor performance.

By including a wide range of assets that don’t move up or down in value in lockstep, an investor can reduce the volatility of their portfolio’s overall return.

For Rachel, choosing investments with lower correlations, such as small-cap stocks in her case, will further diversify her existing portfolio of municipal bonds.

Correlation in Investments

Correlation in the context of investments refers to the degree to which the returns of different assets move in relation to each other. Understanding correlation helps investors decide how to diversify their portfolios effectively.

A correlation value can range from -1 to 1:

• A correlation of 1 means the two investment returns are perfectly in sync.
• A correlation of 0 means the returns are completely independent.
• A negative correlation means the returns move in opposite directions.

Lower or negative correlations between assets mean they don’t move together and are better for diversification, as seen with Rachel's choice of small-cap stocks which exhibit a lower correlation with municipal bonds than large-cap stocks.

Municipal Bonds

Municipal bonds, often called "munis," are debt securities issued by local governments or their agencies. They are used to finance public projects such as schools, highways, and infrastructure improvements.

Muni bonds are popular among investors for a few key reasons:

• They generally offer tax-exempt interest income, which can be beneficial for investors in higher tax brackets.
• They are considered lower-risk investments because they are backed by the revenue-generating capabilities of local governments.

However, muni bonds can be affected by changes in interest rates and the fiscal health of the issuing municipality.

To diversify a heavy position in municipal bonds, Rachel should consider adding investments that have a low or negative correlation with munis, like small-cap stocks.

Large-cap Stocks

Large-cap stocks refer to shares of companies with a market capitalization typically over $10 billion. These are well-known, established companies with a history of stability and consistent growth.

Investing in large-cap stocks can offer several benefits:

• Steady growth and potential dividends.
• Less volatility compared to smaller companies.

However, they may offer lower potential for rapid growth compared to small-cap stocks. In Rachel's case, large-cap stocks have a higher correlation of 0.50 with her municipal bonds, making them less optimal for diversification if lower correlation is desired.

Small-cap Stocks

Small-cap stocks are shares of companies with a market capitalization generally between $300 million and $2 billion. These companies are often newer or underdeveloped compared to large-cap stocks, offering both higher risk and potential for higher rewards.

Here's why small-cap stocks can be appealing:

• Potential for significant growth and high returns.
• More opportunities for capital appreciation compared to larger, more established companies.

In the context of Rachel’s investment strategy, small-cap stocks are particularly beneficial due to their lower correlation of 0.21 with municipal bonds. This helps achieve greater diversification, as their returns are less likely to move in tandem with her existing portfolio.