Equity Markets and Stock Instruments › Sources of Equity Returns

Equity returns come from two sources: capital appreciation and dividend income. Understanding these components helps in constructing return expectations and analyzing historical performance. The relative importance of each component varies across stock types and time periods, making this decomposition essential for understanding what drives portfolio returns.

Capital gains arise when you sell a stock for more than you paid. If you buy at $50 and sell at $60, your capital gain is $10 per share, or 20%. This intuitive calculation forms the foundation for measuring investment performance.

$$\text{Capital Gain Return} = \frac{P_{sell} - P_{buy}}{P_{buy}}$$

where:

• $P_{sell}$: the price at which you sell the stock
• $P_{buy}$: the price at which you originally purchased the stock

This formula measures return relative to your initial investment. The denominator anchors the calculation to what you risked. The numerator captures your profit (or loss), and dividing by the purchase price converts this to a percentage that can be compared across investments of different sizes.

For a holding period of multiple periods, you must distinguish between arithmetic and geometric returns. The geometric (compound) return properly accounts for compounding and answers the question: "What constant return, applied each period, would produce the same final wealth?" A simple arithmetic average does not determine the compound result. With no external cash flows, however, permuting the same return factors does not change terminal wealth because multiplication is commutative. Interim values and drawdowns can still differ.

$$R_{geometric} = \left(\prod_{t=1}^{T} (1 + r_t)\right)^{1/T} - 1$$

where:

• $R_{geometric}$: the geometric mean return per observation period; it is annual only when each period is a year
• $T$: the total number of periods
• $r_t$: the simple return in period $t$
• $\prod_{t=1}^{T}$: the product of all terms from period 1 to $T$

The geometric return reflects the actual growth rate of wealth because it captures the multiplicative nature of compounding. Each period's return applies to the accumulated value, not the original investment. The product operation $\prod$ reflects how returns chain together multiplicatively: a 10% gain followed by a 10% loss does not return you to even because the loss applies to a larger base. The $1/T$ exponent converts the total growth factor back to a per-period rate, extracting the equivalent constant growth rate.

For example, if a stock returns +50% then -50%, the arithmetic average is 0%, but the geometric return is approximately -13.4%:

$$R_{geometric} = \sqrt{(1 + 0.50)(1 - 0.50)} - 1 = \sqrt{0.75} - 1 \approx -0.134$$

You started with $100, grew to$150, then fell to $75: a 25$75. The following illustration compares constant 8% returns with alternating +30% and -14% returns; it demonstrates a particular compounding gap, not a universal terminal-wealth ordering based on variance alone.

Dividends distribute cash to shareholders when declared. They are not guaranteed income independent of company value: absent other changes, a distribution reduces the company’s assets and the ex-dividend share price adjusts. Payment timing and amounts vary. Dividend yield measures annual dividends relative to share price:

$$\text{Dividend Yield} = \frac{D_{annual}}{P}$$

where:

• $D_{annual}$: total dividends paid per share over the past year (or projected for the next year)
• $P$: current stock price

Companies vary dramatically in dividend policy. Growth companies often retain profits to fund expansion rather than pay dividends. Investors may seek capital appreciation from these companies, but that does not guarantee higher returns. Mature companies may distribute 50% or more of earnings, having fewer attractive reinvestment opportunities. Some mature businesses pay substantial dividends. US REIT tax qualification generally requires distributions tied to taxable income, not a particular market dividend yield. A company’s dividend policy and its shares’ market yield are separate quantities. Dividend policy can matter to investors seeking current income.

Total return combines both components into a single measure:

$$R_{total} = \frac{P_{end} - P_{start} + D}{P_{start}}$$

where:

• $R_{total}$: the total return over the holding period
• $P_{end}$: the stock price at the end of the period
• $P_{start}$: the stock price at the beginning of the period
• $D$: total dividends received during the holding period

The numerator captures both sources of value, capital appreciation $(P_{end} - P_{start})$ and income $(D)$. Dividing by the starting price converts this to a percentage return on invested capital. Total return answers the question investors care about: "How much wealthier am I?"

This formula assumes dividends are received as cash rather than reinvested. Reinvestment buys additional shares and changes the subsequent wealth path; it does not guarantee a higher terminal value, because those shares can lose value. Financial databases often report total-return indices that assume dividend reinvestment according to the provider’s methodology. Reinvestment dates, withholding-tax assumptions and corporate-action treatment must be checked for the particular series.