Demonstration 1 of 4
News, price, and the normal return
Once a report is in the price, what is left for a trader, and does a public-data rule survive its costs?
A credible report changes the expected payoff, and competing orders move the price to the new payoff discounted at the required return. After that, a buyer earns only the normal return. A backtest that looks profitable before costs can still lose once the spread, fees and financing are paid.
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The share pays one expected payoff in a year and investors require a 10 percent return, so the benchmark price is the payoff divided by 1.10. The trading rule earns a gross abnormal return of 0.60 percent per trade before the bid-ask spread, fees of 0.25 percent and financing of 0.15 percent.
Predict first. At what bid-ask cost does the 0.60 percent rule exactly break even?
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Constructed example: the chapter's hypothetical share (payoffs 88 and 93.50, required return 10 percent, costs 0.30, 0.25 and 0.15 percent) is the book's; the payoff 99 and bid-ask costs of 0.10 and 0.20 percent are added for comparison.
Calculated values
- Price before report
- $80.00
- Benchmark price after report
- $85.00
- Expected return at new price
- 10.00%
- Net abnormal return
- -0.10%
With an expected payoff of 93.50 the benchmark price is 93.50/1.10 = 85.00, so the price must rise by 5.00 dollars, from 80.00 to 85.00. A buyer at 85.00 expects 93.50/85.00 - 1 = 10.00%, the normal return. Net abnormal return is 0.60 - 0.30 - 0.25 - 0.15 = -0.10 percent, so the public-data rule falls short of the benchmark by 0.10 percent per trade.
Worked steps
- Old price = 88/1.10 = 80.00
- New price = 93.50/1.10 = 85.00
- Return at new price = 93.50/85.00 - 1 = 10.00%
- Net = 0.60 - 0.30 - 0.25 - 0.15 = -0.10%
Use the idea
Before acting on a public signal, subtract every implementation cost from its gross abnormal return; only a positive net result says the price left something on the table.
Where the conclusion applies
Risk is unchanged by the report, the required return is fixed at 10 percent, and the costs are per trade. A negative net result concerns this signal and these costs only; it does not prove markets efficient in every form.
Check your understanding: If the report raises the expected payoff to 99, what is the new benchmark price?
Chapter 46 source: section "Efficient-market hypothesis".
Demonstration 2 of 4
Noise traders and the margin call
Why does a trader who knows the claim is worth 100 still hesitate to short it at 118?
The short is right about value but can be wrong about the path. If noise traders push the price higher before maturity, the marked loss can exhaust capital and force a close at the worst price. A smaller position survives the mark but corrects the mispricing less, which lets it persist.
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A claim pays a certain 100 dollars in two years and trades at 118. A trader with 45 dollars of capital shorts a number of claims. After one year sentiment takes the price to 95 or to the euphoric price with equal probability, and losses must be covered from capital at that mark.
Predict first. With half a claim short and a euphoric price of 190, does the position survive the mark?
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Constructed example: the chapter's hypothetical claim (value 100, price 118, marks 95 and 165, capital 45, positions of 1 and 0.5) is the book's; the size 0.25 and euphoric prices 140 and 190 are added for comparison.
Calculated values
- Marked P/L if price falls
- $23.00
- Marked P/L if price rises
- -$47.00
- Expected marked P/L
- -$12.00
- Forced close
- yes
- Profit at maturity
- none (closed at 165)
Short 1.00 claim at 118. If the price falls to 95 the mark is 1.00(118 - 95) = 23.00; if it rises to 165 the mark is 1.00(118 - 165) = -47.00. Expected marked P/L is 0.5(23.00) + 0.5(-47.00) = -12.00. The loss of 47.00 exceeds the 45 dollars of capital, so the broker closes the short at 165 and the later fall to 100 no longer helps.
Worked steps
- Fall: 1.00(118 - 95) = 23.00
- Rise: 1.00(118 - 165) = -47.00
- Expected: 0.5(23.00) + 0.5(-47.00) = -12.00
- Loss 47.00 > capital 45: forced close
Use the idea
Size a convergence trade so that a plausible adverse mark fits inside the capital you can post, and accept that the smaller size earns less if you are right.
Where the conclusion applies
Two equally likely sentiment states, no interest on margin, and a broker who demands the full marked loss at year one. A longer funding horizon or no interim margin removes the forced close.
Check your understanding: With size 0.5 and a euphoric price of 190, what is the marked loss and does the short survive?
Chapter 46 source: section "Noise-trader risk".
Demonstration 3 of 4
Momentum long-short
How much of a momentum spread survives costs, and what happens when the market reverses?
The long leg earns the winners' return and the short leg loses whatever the losers gain, so the dollar result is the leg times the return spread. Costs come off every period, and a reversal turns the same construction into a large loss.
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The investor buys 400,000 dollars of past winners and shorts 400,000 dollars of past losers. MOM is the winners' return minus the losers' return over the holding period; costs are a percent of one leg.
Predict first. In the reversal with 4 percent costs, does the strategy lose more or less than 15 percent of a leg?
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Constructed example: the chapter's hypothetical portfolio (legs of 400,000, returns 8 and 2 percent, reversal -4 and 10 percent, costs 4 percent) is the book's; costs of 0 and 2 percent are added for comparison.
Calculated values
- Long leg
- $32,000
- Short leg
- -$8,000
- Gross profit
- $24,000
- MOM
- 6%
- Net return
- 2%
Long side: 400,000 x 0.08 = 32,000. Short side: -400,000 x 0.02 = -8,000. Gross 24,000, so MOM = 8% - 2% = 6%. After costs of 4% the net is 6% - 4% = 2%, a gain of $8,000 on one leg.
Worked steps
- Long: 400,000 x 0.08 = 32,000
- Short: -400,000 x 0.02 = -8,000
- MOM = 8% - 2% = 6%
- Net = 6% - 4% = 2%
Use the idea
Judge a momentum rule by its spread net of turnover, spreads, impact and borrow charges, across many periods including reversals, not by one good interval.
Where the conclusion applies
Equal dollar legs, one holding period, costs as a flat share of one leg. One interval does not estimate the population effect.
Check your understanding: In the reversal with 2 percent costs, what is the net return?
Chapter 46 source: section "Momentum effect".
Demonstration 4 of 4
Redemptions force the arbitrageur to sell
Why can a wider discount lead an arbitrage fund to sell instead of buy?
Losses shrink equity, clients withdraw part of what is left, and once cash is gone the manager must sell the mispriced asset into the falling market. The discount widens just as corrective demand is withdrawn.
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The fund has 1,000,000 dollars of equity, holds 10,000 units bought at 80 and 200,000 dollars of cash, and values the asset at 100. After a price shock, clients redeem a share of the remaining equity; cash pays first and units are sold at the shock price for the rest.
Predict first. With 50 percent redemptions, does a deeper drop to 50 raise or lower the number of units sold?
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Constructed example: the chapter's hypothetical fund (equity 1,000,000, 10,000 units at 80, cash 200,000, shock price 60, redemptions of half and the lockup case of none) is the book's; shock prices 70 and 50 and a 25 percent redemption are added for comparison.
Calculated values
- Position loss
- $200,000
- Equity after loss
- $800,000
- Redemption
- $400,000
- Units sold
- 3,333.33
The position loses 10,000(80 - 60) = 200,000, so equity falls to 800,000. Clients redeem 50% of it, 400,000. Cash covers 200,000, so the manager sells 200,000/60 = 3,333.33 units at the depressed price. The value estimate of 100 has not changed; the funding contract drives the sale.
Worked steps
- Loss = 10,000(80 - 60) = 200,000
- Equity = 1,000,000 - 200,000 = 800,000
- Redemption = 0.50 x 800,000 = 400,000
- Units sold = max(0, 400,000 - 200,000)/60 = 3,333.33
Use the idea
Match an arbitrage strategy to funding that cannot run when the mispricing deepens: lockups, no leverage, or enough cash for the worst plausible redemption.
Where the conclusion applies
Redemptions are a fixed share of post-loss equity, cash pays first, and sales happen at the shock price. Patient funding fixes the path problem but cannot make the 100 estimate true.
Check your understanding: At a price of 50 with 50 percent redemptions, how many units must be sold?
Chapter 46 source: section "Limits to arbitrage".