BUS 315

The statistics behind every return

Name: Business Tutor
Address: Burnaby, BC, CA
Telephone: +1-604-916-5838
Price range: C$30–C$129

What did a stock earn, what might it earn, how much does it swing, and does it move with other stocks and the market? The tools the rest of the course leans on, one step at a time.

Part 1 · Returns and expected value · Step 1 of 12

What did the stock earn? The holding-period return

You buy one share for $50. A year later it trades at a new price, P₁, and it has paid you a cash dividend, D₁. The holding-period return (HPR) adds both parts of what you earned, the price change and the dividend, and divides by what you paid, P₀.

Try it: Drop the year-end price below $50, then raise the dividend. The price fell, yet the HPR can still be positive.

Price one year later, P₁$53

Dividend received, D₁$1.50

HPR

9.00%

Capital gain yield

6.00%

Dividend yield

3.00%

Capital gain yield plus dividend yield is the HPR. Both are measured against the $50 you paid, so they simply add.

R = (P₁ − P₀ + D₁) ÷ P₀ = ($53 − $50 + $1.50) ÷ $50 = 9.00%

Price change plus dividend, over what you paid.

6.00% capital gain yield + 3.00% dividend yield = 9.00%

The same return, split into its two parts.

Check yourself

You buy a share at $40. A year later it trades at $38, and it paid a $3 dividend. Your HPR is…

Question 1 of 5CoreTutorial question from the slides

One stock: last year's return and next year's spread

You bought a share for $100. A year later it trades at $108, and it paid a $2 dividend along the way. For next year, an analyst gives three scenarios: a weak economy (probability 20%) with a return of −15%, a normal economy (50%) with 8%, and a strong economy (30%) with 20%.

What was last year’s holding-period return?
What is next year’s expected return?
Find the variance and the standard deviation of next year’s return.
A fund always earns Y = 2R + 3%, where R is this stock’s return. Find E[Y] and SD(Y).

Given

Last year

Price paid$100

Price one year later$108

Dividend received$2

Next year

	Probability	Return
Weak economy	20%	−15%
Normal economy	50%	8%
Strong economy	30%	20%

The fund

Multiplier, b2

Fixed amount added, a3%

Solution

Next year’s return: the probability of each outcome

Read the question and the givens first. Try the first part yourself, then press Start solving and open the working to check.

a. Holding-period return

b. Expected return

c. Variance

c. SD

d. Expected return of Y

d. SD of Y

Midterm coming up and correlation still feels fuzzy?

Bring your problem sets. We work through them together until every type feels routine.

Book a session Next toolNext: Risk preferences and capital allocation

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The statistics behind every return

What did the stock earn? The holding-period return

One stock: last year's return and next year's spread

Midterm coming up and correlation still feels fuzzy?

Questions, answered.

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