What is a return

Okay, so I’m hearing the word "return" a lot, especially around tax season, and when people are talking about shopping. I think I get the gist, but I want to be sure I really understand.

Specifically, I’m confused about these things:

• What’s the difference between a "return" in the context of taxes versus a "return" when you’re talking about returning something to a store? Are they completely unrelated?
• If I buy something online and then send it back, is that always called a "return," or is there another term for that sometimes? Like maybe "exchange" if I’m getting a different size?
• People sometimes talk about "returns" in investing. How does that fit in? Like, what’s a "good" return on an investment versus a "bad" one? How does it relate to risk?
• If I’m filling out my taxes, what exactly am I returning? Is it just the forms? And what happens if I don’t return them?
• Basically, can someone just give me a clear, simple explanation of all the different ways the word "return" is used, and what it means in each context? I want to sound like I know what I’m talking about!

Answer

In finance and economics, a return represents the gain or loss on an investment over a specific period, expressed as a percentage of the initial investment’s cost. It’s a fundamental metric used to evaluate the performance of investments, assess risk, and compare different investment opportunities. The return can be positive (a profit) or negative (a loss).

Components of a Return:

A return can be composed of several elements, depending on the type of investment:

• Capital Appreciation (or Depreciation): This is the change in the market value of the investment. If you buy a stock for $100 and sell it for $120, the capital appreciation is $20. Conversely, if you sell it for $80, the capital depreciation is $20.

• Income: Some investments generate periodic income, such as:
  • Dividends: Payments made by companies to their shareholders, usually from profits.
  • Interest: Payments made by borrowers (e.g., bond issuers, banks) to lenders.
  • Rent: Income generated from owning and leasing out real estate.

Calculating Return:

The basic formula for calculating a simple return is:

Return = (Ending Value - Beginning Value + Income) / Beginning Value

This result is typically multiplied by 100 to express the return as a percentage.

For example:

Suppose you invest $1,000 in a stock. After one year, the stock is worth $1,100, and you received $50 in dividends. The return is calculated as follows:

Return = ($1,100 - $1,000 + $50) / $1,000 = $150 / $1,000 = 0.15

Expressed as a percentage: 0.15 * 100 = 15%

Therefore, the return on your investment is 15%.

Types of Returns:

Several variations and refinements exist for calculating and expressing returns, addressing different complexities and considerations:

• Simple Return: The basic calculation described above, suitable for short periods.
• Annualized Return: Converts a return earned over a period less than a year into an equivalent annual rate. This allows for easier comparison of investments with different durations. For example, a 5% return earned over 6 months is annualized by approximately doubling it to 10%. The precise calculation is more complex, accounting for compounding.
• Holding Period Return (HPR): The total return received from an asset or portfolio over the entire period that it was held by an investor.
• Total Return: The overall return on an investment, encompassing both income and capital appreciation.
• Risk-Adjusted Return: Measures the return relative to the amount of risk taken. Examples include the Sharpe Ratio, Treynor Ratio, and Jensen’s Alpha. These metrics penalize investments with higher volatility (risk) if they don’t produce commensurately higher returns.
• Real Return: The return adjusted for inflation. This reflects the true purchasing power gained from the investment. Calculated as: Real Return = (Nominal Return - Inflation Rate) / (1 + Inflation Rate). An approximate calculation often used is: Real Return ≈ Nominal Return - Inflation Rate.
• Arithmetic Mean Return: The simple average of a series of returns over multiple periods. It’s easy to calculate but can be misleading if returns are highly volatile.
• Geometric Mean Return: A more accurate measure of average return over multiple periods, especially when returns fluctuate significantly. It considers the effects of compounding. It is calculated by taking the nth root of the product of (1 + each return).
• Time-Weighted Return (TWR): A method of calculating investment performance that removes the impact of cash flows into and out of the portfolio. This is often used to evaluate the performance of fund managers, as it focuses on their investment decisions rather than the timing of investor deposits or withdrawals.
• Dollar-Weighted Return (DWR): Also known as the Internal Rate of Return (IRR), it considers the timing and size of cash flows. It reflects the actual return earned by the investor, taking into account when money was invested. It is affected by the timing of contributions and withdrawals.

Factors Affecting Returns:

Numerous factors can influence the return on an investment:

• Market Conditions: Overall economic conditions, interest rates, inflation, and geopolitical events.
• Company Performance: For stocks, the profitability, growth prospects, and management effectiveness of the underlying company.
• Industry Trends: Changes in technology, consumer preferences, and regulations affecting the industry in which the company operates.
• Risk Tolerance: Higher-risk investments typically have the potential for higher returns, but also the potential for greater losses.
• Investment Horizon: The length of time an investment is held. Longer investment horizons generally allow for greater potential returns, but also greater exposure to market fluctuations.
• Inflation: Erodes the purchasing power of returns.
• Taxes: Can significantly reduce after-tax returns.
• Fees and Expenses: Investment management fees, brokerage commissions, and other expenses reduce the net return to the investor.
• Liquidity: The ease with which an investment can be bought or sold without affecting its price. Illiquid investments may offer higher potential returns but also carry greater risk.

Importance of Returns:

Understanding and calculating returns is crucial for:

• Investment Decision-Making: Comparing the potential profitability of different investment options.
• Performance Evaluation: Assessing the success of past investment decisions.
• Financial Planning: Projecting future investment growth and achieving financial goals.
• Risk Management: Understanding the relationship between risk and return.
• Benchmarking: Comparing investment performance against relevant market indices or peer groups.

In summary, the return is a fundamental concept in finance, representing the profit or loss on an investment. A comprehensive understanding of the various types of returns, the factors that influence them, and their applications is essential for making informed investment decisions and achieving financial success.