The Myth Of Identical Investments: Unraveling The Unique Factors That Shape Your Portfolio

Two different investments will be the same when they have exactly opposite returns. If one investment generates income, and the other generates losses, the overall value of the two investments will remain the same.

Opposite returns

When two equal investments have exactly opposite returns, the total value of both investments remains the same. This is because one investment is generating income while the other is generating losses, and so the overall value of the two investments balances out.

In finance, a return is a profit on an investment. It can be measured in absolute terms, such as a dollar amount, or as a percentage of the amount invested. A loss instead of a profit is described as a negative return. The return on investment (ROI) is a measure of investment performance and is calculated by finding the return per dollar invested.

The direct method to calculate the return over a single period of any length of time is:

> {\displaystyle R={\frac {V_{f}-V_{i}}{V_{i}}}}

Where:

• {\displaystyle R} = return
• {\displaystyle V_{f}} = final value, including dividends and interest
• {\displaystyle V_{i}} = initial value

For example, if someone purchases 100 shares at a starting price of 10, the starting value is 1,000. If the shareholder then collects $0.50 per share in cash dividends, and the ending share price is $9.80, then at the end the shareholder has $50 in cash, plus $980 in shares, totalling a final value of $1,030. The change in value is $1,030 − $1,000 = $30, so the return is {\displaystyle {\frac {30}{1,000}}=3\%}.

The overall period may be divided into multiple sub-periods, each beginning where the previous one ended. In this case, the return over the overall period can be calculated by combining the returns within each of the sub-periods.

When the return is calculated over a series of sub-periods, the return in each sub-period is based on the investment value at the beginning of that sub-period. If there are no inflows or outflows during the period, the holding period return in the first period is:

> {\displaystyle R_{1}={\frac {B-A}{A}}}

Where:

• {\displaystyle R_{1}} = holding period return in the first period
• {\displaystyle A} = value of the investment at the beginning
• {\displaystyle B} = value of the investment at the end of the first period

If the gains and losses are reinvested, the value of the investment at the start of the second period is {\displaystyle B}. If the value of the investment at the end of the second period is {\displaystyle C}, the holding period return in the second period is:

> {\displaystyle R_{2}={\frac {C-B}{B}}}

Multiplying together the growth factors in each period:

> {\displaystyle (1+R_{1})(1+R_{2})={\frac {B}{A}}{\frac {C}{B}}={\frac {C}{A}}}

> {\displaystyle (1+R_{1})(1+R_{2})-1={\frac {C}{A}}-1={\frac {C-A}{A}}}

This is the holding period return over the two successive periods. This method is called the time-weighted method, or geometric linking, or compounding together the holding period returns in the two successive sub-periods.

Extending this method to {\displaystyle n} periods, assuming reinvestment of returns, if the returns over {\displaystyle n} successive time sub-periods are {\displaystyle R_{1},R_{2},R_{3},\cdots ,R_{n}}, then the cumulative return or overall return {\displaystyle R} over the overall time period using the time-weighted method is:

> {\displaystyle 1+R=(1+R_{1})(1+R_{2})\cdots (1+R_{n})}

Logarithmic returns are symmetric, while ordinary returns are not. This means that positive and negative percent ordinary returns of equal magnitude do not cancel each other out, but logarithmic returns of equal magnitude but opposite signs will cancel each other out. For example, an investment of $100 that yields an arithmetic return of 50% followed by an arithmetic return of −50% will result in $75, while an investment of $100 that yields a logarithmic return of 50% followed by a logarithmic return of −50% will come back to $100.

Generating income

There are two common investment strategies: investing for growth or investing for income. This section will focus on the latter. Income investments pay out dividends or interest to the investor based on a set schedule.

• Dividend-yielding stocks: Some companies pay out a dividend, or a portion of their profits, to stockholders. Dividends are not fixed and can change or be eliminated without much notice. The dividend yield can also vary due to share price increases or decreases.
• Preferred stock: This is distinct from common stock and is not offered by all companies. Preferred stocks offer dividends that aren't guaranteed but must be paid before dividends on common stock. They have various terms and features that can impact future income.
• Fixed-rate capital securities (FRCS): These hybrid securities combine the features of corporate bonds and preferred stock. They carry the creditworthiness of the issuer and usually have a stated maturity. However, they may defer or suspend interest payments if the issuer experiences financial difficulties.
• Equity income funds: These funds invest in shares of companies that pay dividends and can offer an attractive yield, along with potential for conservative capital appreciation.
• Asset allocation funds: These funds offer diversification across multiple asset classes, including domestic and international stocks, fixed income, and short-term investments.
• Mutual funds and exchange-traded funds (ETFs): These funds can provide diversified access to a range of securities and reduce transaction costs.
• Bonds: When looking for income, the interest paid by bonds may be more important than price fluctuations. Treasury bonds, issued and backed by the US government, are among the safest income-generating investments. Municipal bonds, issued by state and local governments, offer income that is usually exempt from federal income taxes and may also be exempt from state and local taxes.
• Build a bond ladder: This involves purchasing bonds of varying maturities, such as short, medium, and long durations. This strategy provides predictable payments and the option to reinvest at current market rates as each bond matures. It also increases liquidity, as shorter-term bonds offer quicker access to cash.

It's important to note that investing in stocks and bonds involves risks, including the loss of principal. Before investing, consider the funds' investment objectives, risks, charges, and expenses.

Generating losses

When two equal investments have exactly opposite returns, the total value of both investments will remain the same over time. This is because, while one investment is generating income, the other is generating losses, and so the overall value of the two investments balances out.

To generate losses, an investment must be losing value over time. This can happen for a variety of reasons, such as poor financial performance, market downturns, or mismanagement. It's important to note that generating losses is not the same as depreciating assets, as depreciating assets can still have value and generate income. In this case, we are specifically looking at investments that are losing value.

For example, let's say you have two investments of $10,000 each. Investment A generates a 10% return, resulting in a value of $11,000. Meanwhile, Investment B loses 10% of its value, resulting in a value of $9,000. In this case, the total value of your investments remains the same, as the gains from Investment A are offset by the losses from Investment B.

It's worth noting that this scenario assumes that the two investments are equal in value and have exactly opposite returns. If the investments are not equal or the returns are not perfectly opposite, the total value may fluctuate. Additionally, this scenario assumes a simplified financial model, and real-world investments can be influenced by numerous complex factors.

Total value

When two investments are equal and have exactly opposite returns, the total value of both investments will remain the same over time. This is because, while one investment is generating income, the other is generating losses, and so the overall value of the two investments combined stays the same.

For example, imagine you have two investments, A and B, and they are equal in value. Over time, investment A generates a return of $1000, while investment B generates a loss of $1000. The total value of your investments has therefore not changed, as the gains from A are cancelled out by the losses from B.

This scenario assumes that the two investments are always of equal value and that their returns are always exactly opposite, which is unlikely to occur in reality. However, it demonstrates the principle that when two investments have opposite performances, their combined value can remain the same.

Investments

There are various types of investments, each carrying different levels of risk and potential reward. Some common types of investments include stocks, bonds, real estate, mutual funds, exchange-traded funds (ETFs), and commodities.

When considering two different investments, it is important to understand that the total value of both investments can remain the same over time if one investment generates income while the other generates losses. This is because the overall impact of the two investments can offset each other, resulting in a net-zero change.

However, in the long term, different investments can yield varying results due to factors such as market performance, compound interest, and the specific characteristics of the investments.

For example, consider two individuals who invest in different stocks. Over time, the performance of these stocks will depend on various economic factors, company-specific news, and market sentiment. One stock may outperform the other due to stronger financial results, favourable market conditions, or other factors.

Additionally, the concept of compound interest can significantly impact the growth of investments over time. Compound interest occurs when the earnings generated by an investment are reinvested, leading to exponential growth. As a result, two different investments with the same initial value can diverge significantly in the long run due to the effects of compound interest.

It is also important to consider the risk associated with different investments. Risk and return are generally correlated, with higher-risk investments offering the potential for higher returns. Therefore, two investments with different risk profiles may result in divergent outcomes over time.

In summary, while two different investments may yield the same results in certain scenarios, their performance can vary significantly over time due to market conditions, compound interest, and the inherent risk and return characteristics of the investments.

Frequently asked questions