F. Calc and Interp Lev. Ratio, ROR on a margin trans., sec. price at margin call Flashcards
SchweserNotes: Book 4 p.211 CFA Program Curriculum: Vol.5 p.41
Leverage, a margin transaction
‘On margin’ - Security purchases are financed via ‘margin loans’ borrowed funds which create ‘levered positions’ that are charged at the call money rate - interest rate paid. • Equity is the traders contributed money but they bear full risk (financial - additional risk from the use of borrowed funds + others) no matter the capital structure of their security purchases.
Addtional notes: Margin Increases Risk: A given level of equity supports more risk when leverage is greater because more securities can be bought by borrowing.
SchweserNotes: Book 4 p.211 CFA Program Curriculum: Vol.5 p.41
Financial Leverage (Leverage) = Asset value / equity position value
The leverage ratio is the value of the asset divided by the value of the equity position. Higher leverage ratios indicate greater risk.
Aka: the ratio of the value of the position to the value of the equity investment in it.
SchweserNotes: Book 4 p.211 CFA Program Curriculum: Vol.5 p.41
Total Return on a Margined Position
The return on a margin transaction is the increase in the value of the position after deducting selling commissions and interest charges, divided by the amount of funds initially invested, including purchase commissions. • Suppose that a buyer buys stock on margin and holds the position for some period, during which time the stock pays a dividend. • The total return on the margined position is equal to the profit divided by the initial equity investment. • The profit is the trading gain or loss (change in price times shares purchased) plus dividends received minus margin interest paid minus purchase and sales commissions. • The initial investment is the cost of the position (including any purchase commissions) minus the value of the margin loan.
An investor purchases 200 shares of Mertz, Inc. on margin. The shares are trading at $40. Initial and maintenance margins are 50% and 25%. If the investor sells the stock when the price rises to $50 at year-end, the return on the investment would be closest to:
Profit = 10,000 – 8,000 = 2,000 Return = 2,000 / 4,000 = 50%
Fin. Lev = Eq. / Assets
Total Return on a Margin Position = Assets (profit) / Eq. (Margin position - equity * initial margin)
An investor purchases 200 shares of Rubble, Inc. on margin. The shares are trading at $40. Initial and maintenance margins are 50% and 25%. If the company pays a dividend of $0.75 and the investor sells the stock at year-end for $50 per share, the return on the investment would be closest to:
Dividend income = 0.75 × 200 = $150
Profit = 10,000 – 8,000 + 150 = 2,150
Return = 2,150 / 4,000 = 53.75%
-Include dividence income to profit before dividing profit by the equity, rather, the product of the margin position - equity * initial margin
Lynne Hampton purchased 100 shares of $75 stock on margin. The margin requirement set by the Federal Reserve Board was 40%, but Hampton’s brokerage firm requires a total margin of 50%. Currently the stock is selling at $62 per share. What is Hampton’s return on investment beforecommission and interest if she sells the stock now?
Hampton originally purchased 100 shares at $75 for a total value of $7500. Half of the value ($3750) was borrowed and Hampton paid cash for the other half. The current total market value of the stock is $6200. If Hampton sells her holdings she will have $2450 left after she pays off the loan. Hampton’s return on her original investment is:
$2450/3750 – 1 = 0.65 – 1 = -0.35 = -35%.
SchweserNotes: Book 4 p.211 CFA Program Curriculum: Vol.5 p.41
Margin Requirements for Purchases (The margin requirement represents the amount of money an investor must put down on the purchase.)
• ‘Margin’ is a the value of the position that is represented by equity. – The margin ratio is the inverse of the leverage ratio.
Traders must meet an initial margin requirement when buying.
Becky Kirk contacted her broker and placed an order to purchase 1,000 shares of Bricko Corp. stock at a price of $60 per share. Kirk wishes to buy on margin. Assuming the margin requirement is 40%, how much money does Kirk have to pay up front to make the purchase?
So Kirk must put $24,000 down ($60,000 x .40 = $24,000) and can borrow the balance.
If an investor buys 100 shares of a $50 stock on margin when the initial margin requirement is 40%, how much money must she borrow from her broker?
An initial margin requirement of 40% would mean that the investor must put up 40% of the funds and brokerage firm may lend the 60% balance. Therefore, for this example (100 shares) * ($50) = $5,000 total cost. $5,000 * 0.60 = $3,000.
SchweserNotes: Book 4 p.211 CFA Program Curriculum: Vol.5 p.41
Maintenance Margins
A minimum required % of equity an investor must hold in his account.
Investors with equity below maintenance recieve a ‘margin call.’ or when prices drop - either way, a deposit of additional equity must be made.
If unsatisifed, the broker sells the position to secure the payment and you’re fucked because you owe the broker for being a dumbass and have 0 equity in your balance.
SchweserNotes: Book 4 p.211 CFA Program Curriculum: Vol.5 p.41
Margin Call Prices
(New value) - (Old value*maintenence margin) - (Margin Loan Repayment) / (Old value*maintenence margin)
97731 Using the following assumptions, calculate the rate of return on a margin transaction for an investor who purchases the stock and the stock price at which the investor would have received a margin call.
where:
P0 = initial purchase price
- The price at which a margin buyer will receive a margin call is is where equity remaining in the position or the ‘maintenance margin’ is = to the margin rate.
- Current equity per share = initial equity per share - L’s since purchase
An investor purchases 100 shares of Lloyd Computer at $26 a share. The initial margin requirement is 50%, and the maintenance margin requirement is 25%. The price below which the investor would receive a margin call is closest to:
26 * (1 - 0.5)/(1 - 0.25) = $17.33.
Not $26,000, but simply $26 or the margin call PRICE, not total value
Market Price Per Share: $32
Number of Shares Purchased: 1,000
Holding Period: 1 year
Ending Share Price: $34
Initial Margin Requirement: 40%
Maintenance margin: 25%
Transaction and borrowing costs: $0
The company pays no dividends
Part 1: Calculate Margin Return:
Margin Return %
= [((Ending Value – Loan Payoff) / Beginning Equity Position) – 1] × 100
= [(([$34 × 1,000] – [$32 × 1,000 × 0.60]) / ($32 × 0.40 × 1,000)) – 1] × 100
= 15.6%
Alternative (Check): Calculate the all cash return and multiply by the margin leverage factor.
[(34,000 – 32,000) / 32,000] × [1 / 0.40] = 6.35% × 2.5 = 15.6%
Part 2: Calculate Margin Call Price:
The formula for the margin call price is:
Margin Call = (original price) × (1 - initial margin) / (1 - maintenance margin)
= $32 × (1 - 0.40) / (1 - 0.25) = approximately $25.60
An investor purchases 100 shares at $75 per share with an initial margin of 50%. Assume there is no interest on the call loan and no transactions fees. If the stock price rises to $112.50, the rate of return to the investor is:
$75/share × 100 shares = $7,500.
50% margin means investor only pays half of the $7,500 in cash, or $3,750, and borrows the remaining $3,750.
Rate of return = (market value – initial investment – margin loan repayment) / initial equity
= ($11,250 – $3,750 (P1*initial margin) – $3,750) / $3,750 = 100%.
Pt+1-(initial value*initial margin) - D1 or ‘Margin Loan Repayment’ / P1
SchweserNotes: Book 4 p.211 CFA Program Curriculum: Vol.5 p.41
Sonia Fennell purchases 1,000 shares of Xpressoh Inc. for $35 per share. One year later, she sells the stock for $42 per share. Xpressoh Inc. pays no dividends. The initial margin requirement is 50%. Fennell’s one-year return assuming an all-cash transaction, and if she buys on margin (assume she pays no transaction or borrowing costs and has not had to post additional margin), are closest to:
*Calc Margin Return
*Calc All Cash Return
All-cash return = 42/35 − 1 = 20%
Margin return = (42 − 35)/[(35)(0.5)] = 40%
Initial when not explicitly stated is P1 - Pt-1 / pt-1(maintenence margin)
Where, P0 = (All-cash return, as there is a t and t1)/(t2)*(1- initial margin)
Rather, all cash return / 1- initial margin = Margin Return
SchweserNotes: Book 4 p.211 CFA Program Curriculum: Vol.5 p.41
An investor purchases stock on 25% initial margin, posting $10 of the original stock price of $40 as equity. The position has a required maintenance margin of 20%. The investor later sells the stock for $45. Ignoring transaction costs and margin loan interest, which of the following statements is most accurate?
Return on invested equity is ($45 – $40) / $10 – 1 = 50%.
The leverage ratio is purchase price / equity = $40 / $10 = 4.
Margin call price is $40 × [(1 – 0.25) / (1 – 0.20)] = $37.50.
