1. Additional Topics Additional items to address: Holding Period Return Short Selling with Margin Requirements

2. Holding Period Return In general, the holding period return for any financial instrument can be defined as: HPR = (Appreciation in Price + Income Received) / Beginning Price So Holding Period Return covers any type of value derived from owning the asset whether reflected as a price increase or in the form of income paid (such as dividends)

3. Holding Period Return Examples: T-Bill purchased for 9925 and matures for face value of 10,000 at the end of 90 days HPR for the 90 day period = 75 / 9925 =.7557% Stock purchased for 100 and grows to 120 after one year, paying a dividend of 5 HPR for year = (20 + 5) / 100 = 25%

4. Holding Period Return We know that the return on financial instruments may not be certain, especially for equities. In these cases, we may consider what the Expected HPR is given the returns we anticipate in different economic scenarios If there are S possible states of the world at the end of the measuring period, with state s having probability p(s), and generating a return of r(s), then Expected HPR = Σ p(s) r(s)

5. Holding Period Return Example: Assume you buy an equity at the beginning of the year for $25 and it pays a dividend of $5 at the end of the year. The following potential scenarios could play out: What is the Expected Holding Period Return? State of the WorldProbabilityPrice at End of Year Large Growth.20$40 Moderate Growth.50$30 Moderate Recession.30$20

6. Holding Period Return Under Large Growth scenario, HPR = (15 + 5) / 25 = 80% Under Moderate Growth scenario, HPR = (5 + 5) / 25 = 40% Under Moderate Recession scenario, HPR = (-5 + 5) / 25 = 0% Expected HPR =.20(80%) +.50(40%) +.30(0%) = 16% + 20% = 36%

7. Short Selling and Margin In the previous class we talked about how it was possible to perform a short sale on a financial instrument by borrowing it from the inventory of a dealer and selling it to a third party The hope is that the instrument declines in price and you can re-supply it to the dealer buy purchasing in the open market at the lower price and make a profit Clearly, the dealer is taking some sort of credit risk when he allows you to borrow the instrument, so he sets up some requirements to protect his interest

8. Short Selling and Margin Initial Margin = Amount required to initiate the trade = Amount generated from sale of borrowed assets PLUS an additional amount to cover the risk that the price of the stock may increase The additional amount is usually a function of the initial value of the trade So if you short sell n shares of a stock valued at time zero at S 0, and the initial margin requirement is u, then the initial value of the sale is n S 0, and the additional initial margin = u n S 0

9. Short Selling and Margin To minimize the credit risk, the dealer will always require that the “investor’s equity position” be at least a fraction v of the market value of the assets (v < u ) This is called the maintenance margin requirement “Investor’s Equity Position” - recall that on a balance sheet, a person’s “equity” or “surplus” is the difference between the assets they own and the liabilities they have promised to fulfill

10. Short Selling and Margin Note that Investor’s Equity = Investor’s Asset – Investor’s Liability = (Gain from short sale + additional initial margin) - Current Market Price of Stock = n S 0 + u n S 0 - n S 1 So dealer requires that n S 0 + u n S 0 - n S 1 > v n S 1

11. Short Selling and Margin Example: Sell Short 100 shares of stock at current price of $65, initial margin requirement = 50%, maintenance margin requirement of 30% So investor sells the 100 shares and receives $6500, plus must also keep an additional $3250 on deposit. Total initial asset = $9750 Maintenance Margin = 30% * 100 * Current Market Price Stock price goes to $70: Investor’s Equity = n S 0 + u n S 0 - n S 1 = $6500 + $3250 - $7000 = $2750 Maintenance Margin = 30% * 100 * 70 = $2100 Since Equity > Maintenance Margin, then no adjustments needed

12. Short Selling and Margin Stock price goes to $80: Investor’s Equity = n S 0 + u n S 0 - n S 1 = $6500 + $3250 - $8000 = $1750 Maintenance Margin = 30% * 100 * 80 = $2400 Since Equity < Maintenance Margin, so an adjustment needed via a margin call Dealer may require that the full initial additional margin of $3250 is re-established

13. Short Selling and Margin At what exact price would a margin call be initiated? Where n S 0 + u n S 0 - n S 1 = v n S 1 Solving for S 1 : S 1 = (n S 0 + u n S 0 ) / (n + v n) In our example: S 1 = ($6500 + $3250 ) / (100 +.3(100)) = $9750 / 130 = $75