Risk and Return: All you need to know

Return

The holding period return (HPR) measures what you earned over a period:

HPR = (Ending price − Beginning price + Income) ÷ Beginning price

Income means dividends for stocks or coupons for bonds.

Example: buy a share at $100, receive a $4 dividend, sell at $110. HPR = (110 − 100 + 4) ÷ 100 = 14%.

Expected return

The future is uncertain, so investors think in scenarios. The expected return is the probability-weighted average of the possible returns:

E(r) = Σ p(s) × r(s)

Risk

Risk is the uncertainty of the return. It’s usually measured by the standard deviation: how widely returns spread around their average. A higher standard deviation means a wider range of possible outcomes, good and bad. See how to calculate expected return and standard deviation.

The risk premium

• The risk-free rate is the return on a safe asset, such as Treasury bills.
• The risk premium is the extra expected return for holding a risky asset: E(r) − risk-free rate.
• The excess return is the actual return minus the risk-free rate.

Investors demand a risk premium because they’re risk-averse: given two investments with the same expected return, they prefer the less risky one.

The risk–return trade-off

Historically, asset classes with more risk have earned more on average:

T-bills → government bonds → corporate bonds → large stocks → small stocks

Each step up has had higher average returns and higher volatility. There’s no free lunch: a higher expected return comes with more risk.

The Sharpe ratio

To compare investments, divide the risk premium by the risk:

Sharpe ratio = (E(r) − Risk-free rate) ÷ Standard deviation

A higher Sharpe ratio means more reward for each unit of risk.

Real vs nominal returns

The nominal return ignores inflation. The real return is roughly the nominal return minus inflation. A 7% return with 3% inflation is about a 4% real return.

Next: how to calculate expected return and standard deviation.