Stock returns explained :- Calc Suite - Complete Calculator

 Stock return is a comprehensive measure of the profit or loss an investor receives from an investment in a company's stock over a specified period. It's typically expressed as a percentage of the initial investment and is a crucial metric for evaluating investment performance.

A stock's total return is composed of two main elements:

1. Capital Gains (or Losses)

This is the appreciation or depreciation in the market price of the stock.

• Gain: Occurs when the selling price (or current market price) is higher than the original purchase price.
• Loss: Occurs when the selling price (or current market price) is lower than the original purchase price.

$$\text{Capital Gain/Loss}=\text{Selling/Current Price}-\text{Purchase Price}$$

2. Income (Dividends)

This is the cash income distributed by the company to its shareholders from its earnings.

• Dividends are paid on a per-share basis and represent a tangible return on the investment, even if the stock price remains unchanged or declines.
• For total return calculation, all dividends received during the holding period are included.

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Key Stock Return Calculations

1. Holding Period Return (HPR)

The HPR is the total return earned on a stock over the entire period it was held.

$$\text{HPR}=\frac{(\text{Current Price}-\text{Purchase Price})+\text{Dividends Received}}{\text{Purchase Price}}$$

Example:

• Purchase Price: $50 per share
• Current Price: $60 per share
• Dividends Received: $2 per share
• HPR=$50($60−$50)+$2​=$50$12​=0.24 or 24%

2. Annualized Return (Geometric Average Return)

The HPR is useful, but to compare the performance of investments held for different lengths of time (e.g., 18 months vs. 5 years), the return must be annualized. The standard method for this is the Geometric Average Return or Compound Annual Growth Rate (CAGR), which accounts for the effect of compounding.

$$\text{Annualized Return}=\left[(1+\text{HPR}{)}^{(1/t)}\right]-1$$

Where $t$ is the holding period in years.

Example (continuing HPR example): If the HPR of 24% was earned over a holding period of 2 years:

$$\text{Annualized Return}=\left[(1+0.24{)}^{(1/2)}\right]-1=(1.24^{0.5})-1\approx 1.1136-1\approx 0.1136\text{ or }11.36\%$$

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Important Concepts for Return Measurement

Arithmetic Mean vs. Geometric Mean

When measuring the average return of a stock over multiple periods (e.g., years), two common methods are used, but they provide different insights:

Feature	Arithmetic Mean Return	Geometric Mean Return (CAGR)
Calculation	Simple average of all periodic returns.	Compounded average return over time.
Interpretation	Best for estimating expected return in a single future period (i.e., forward-looking).	Best for measuring the actual return achieved over multiple periods (i.e., historical return).
Accuracy	Generally overstates the actual long-term compound growth rate, especially with high volatility.	Considered the more accurate measure of investment performance over time because it accounts for compounding.

Rule of Thumb: For historical, multi-period stock performance, the Geometric Mean Return is the preferred and more realistic metric.

The Effect of Compounding

Stock returns often involve compounding, where income (dividends) and gains are reinvested to earn even more return in subsequent periods. The Annualized Return formula inherently captures this effect, providing a true measure of wealth growth.

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Risk and Return

Stock return is inextricably linked to risk. The fundamental principle in finance is the Risk-Return Tradeoff:

• Investments with the potential for higher returns generally carry a higher degree of risk (volatility, potential for loss).
• Stocks, as an asset class, are considered relatively high-risk compared to bonds or cash, but historically, they have also offered the highest long-term returns.