Lecture Overview:

• Calculating Returns
• Quoting returns in this class
• Real return
• Expected return and SD

Calculating Returns

“buy and hold” investment

• Holding period return (HPR) is a measure of return earned over a given investment period.

$$ HPR_t = \frac{P_t+D_t+P_{t-1}}{P_{t-1}} $$

Where:

$P_t$ is investment value at end of holding period.

$P_{t-1}$ is initial investment value.

$D_t$ is the investment income such as dividend, coupon, etc.

• Implicitly assumes the investment income is received at the end of the holding period.
• Called as “realised return” if it has happened.

Lets denote this period return as r.

Now assume we have a sample of returns over multiple T periods for a single asset $(r_1, r_2, r_3, ..., r_t)$

Average returns over time-series:

Arithmetic Average Return, Geometric Average Return

(check book for formulas and examples)