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BUS 315

How much risk should you take?

One risky fund, one safe asset, one investor. Measure the return, describe how the investor feels about risk, then find the mix that suits them best on the capital allocation line.

Part 1 · Measure the return · Step 1 of 12

A stock held for two years, dividends reinvested

$80.00Today1 share × $80$92.40Year 11.05 × $88$92.61Year 21.1025 × $84
your original sharesshares bought with dividends
You buy one share at $80. Each year-end dividend is used straight away to buy more shares at that day's price. Those extra shares then rise and fall with the stock and earn the next dividend too. The holding-period return (HPR) compares what you end with to what you started with.
Try it: Set Year 2's price back to $80, where it started. The HPR is still positive: you own more shares than you bought.
Year 1 price (after the dividend)$88
Year 1 dividend per share$4.40
Year 2 price (after the dividend)$84
Year 2 dividend per share$4.20
Amount invested
Two-year HPR
15.76%
Shares owned
1.1025
Ending wealth
$92.61
The ending wealth already includes the reinvested dividends (as extra shares). Do not add the dividends again: that would count them twice.
Year 1: 1 + $4.40 ÷ $88 = 1.05 shares, worth $92.40
The dividend buys shares at the year-end price.
Year 2: 1.05 × $4.20 = $4.41 buys 0.0525 more → 1.1025 shares, worth $92.61
Every share, including the new ones, earns the year 2 dividend.
HPR = ($92.61 − $80) ÷ $80 = 15.76%
Check yourself
You end with more shares than you bought, and the price ends where it started. Your HPR is…

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