- Text
- Returns,
- Monotonicity,
- Strict,
- Increasing,
- Binary,
- Strategies,
- Statistics,
- Stocks,
- Prices,
- Underlying,
- Stochastic,
- Discount,
- Factor

Monotonicity of the stochastic discount factor and expected option ...

Table IAverage Returns for **option** strategies on **the** S&P 500 indexThis table reports weekly average buy **and** hold returns for some **option** trading strategieson **the** S&P 500 index that are special cases **of** **the** log-concave class **of** payout functions.Strike groups are defined using **the** following procedure: For each buying date we find **the****option** contract which has a strike price that is closest to **the** price **of** **the** underlying security**and** assign that to strike group 3. The next two higher strikes are assigned to groups 4**and** 5 respectively. Similarly, **the** previous two lower strikes are assigned to groups 1 **and** 2respectively. Returns are calculated based on prices observed on Tuesdays. “ ∗ ” indicates**the** strike group for which **the** average return difference between **the** strike group **and** itsimmediate lower strike group is negative **and** statistically significant at **the** 5% level thusviolating strict monotoncity.Table I: Average returns by strike groupPanel A: call returnsStrike Group 1 2 3 4 5Average returns 0.024 0.028 0.036 0.042 0.046t statistics 0.774 0.822 0.927 0.899 0.830Panel B: put returnsStrike Groups 1 2 3 4 5Average returns -0.140 -0.120 -0.105 -0.090 -0.078t statistics -3.172 -2.834 -2.618 -2.419 -2.258Panel C: binary call returnsStrike Groups 1 2 3 4 5Average returns -0.029 0.004 -0.008 0.041 0.042t statistics -1.550 0.208 -0.344 1.488 1.257Panel D: bullish call returnsStrike Groups 1 2 3 4 5Average returns 0.004 -0.008 0.041 0.042 0.068t statistics 0.208 -0.344 1.488 1.257 1.706Panel E: (modified) butterfly spread returnsStrike Groups 1 2 3 4 5Average returns 0.470 0.507 0.276 ∗ 0.392 0.525t statistics 2.840 4.008 2.584 2.803 4.38945

Table IIAverage Return Differences for **option** strategies on individualstocksThis table reports differences **of** weekly average buy **and** hold returns for some **option** tradingstrategies that are special cases **of** **the** log-concave class **of** payout functions. Strike groupsare defined using **the** following procedure: For each underlying stock **and** buying date wefind **the** **option** contract which has a strike price that is closest to **the** price **of** **the** underlyingstock **and** assign that to strike group 3. The next two higher strikes are assigned to groups4 **and** 5 respectively. Similarly, **the** previous two lower strikes are assigned to groups 1 **and** 2respectively. The **option**s must satisfy **the** following conditions to be included in **the** sample:(1) The bid price is strictly larger than $0.125, (2) **the** ask price is greater than **the** bid price,(3) **the** underlying stock does not have an ex-dividend date prior to maturity **and** (4) **the****option** prices satisfies a no-arbitrage restriction. R s denotes **the** return on **the** underlyingstock **and** R f denotes **the** risk-free rate.Table II: Average return differences by strike groupPanel A: call returnsStrike Groups 1-R s 2 -1 3 -2 4 -3 5 -4Average returns 0.010 0.006 0.014 0.102 0.070t statistics 2.33 2.25 2.23 8.81 3.82Skewness adjusted t statistics 2.30 2.25 2.28 15.07 6.27Panel B: put returnsStrike Groups 2 -1 3 -2 4 -3 5 -4 R f - 5Average returns 0.002 -0.004 0.013 0.012 0.016t statistics 0.07 -0.36 0.97 1.73 2.27Skewness adjusted t statistics 0.17 -0.39 0.85 1.63 2.19Panel C: butterfly spread returnsStrike Groups 2 -1 3 -2 4 -3 5 -4Average returns - -0.009 0.079 0.187 0.133t statistics - -0.99 4.36 4.14 1.98Skewness adjusted t statistics - -1.01 4.62 7.14 2.26Panel D: binary call returnsStrike Groups 1-R f 2 -1 3 -2 4 -3 5 -4Average returns 0.049 0.000 0.006 0.059 0.225t statistics 8.19 0.04 0.54 3.30 3.04Skewness adjusted t statistics 7.68 0.04 0.63 3.70 5.63Panel E: (modified) bullish call returnsStrike Groups 2 -1 3 -2 4 -3 5 -4Average returns - 0.097 0.047 0.185 0.099t statistics - 8.47 3.19 9.49 2.94Skewness adjusted t statistics - 5.31 4.07 9.82 6.0046

- Page 1: Monotonicity of the stochastic disc
- Page 4 and 5: 500 results, our empirical analysis
- Page 6 and 7: I. Characterization of SDF Monotoni
- Page 8 and 9: The intuition for the equivalence o
- Page 10 and 11: consumption in the two middle state
- Page 12 and 13: The first two examples below presen
- Page 14 and 15: tional to the slope of m (), as is
- Page 16 and 17: strict monotonicity because it requ
- Page 18 and 19: eturns, and the sample reduces to 1
- Page 20 and 21: skewness of option returns (most OT
- Page 22 and 23: money.Assuming only differentiabili
- Page 24 and 25: against the alternative hypothesis
- Page 26 and 27: in an increasing across strike grou
- Page 28 and 29: Further compounding the heterogenei
- Page 30 and 31: is equivalent to0 > E ( mS T 1 {ST
- Page 32 and 33: The inverse of the expected return
- Page 35 and 36: Using integration by parts:Cov (Y,
- Page 37 and 38: Equation B3 is the skewness adjuste
- Page 39 and 40: where we have used, for any k ∈ {
- Page 41 and 42: Brown, David, and Jens Carsten Jack
- Page 43 and 44: Huang, C., and R. Litzenberger, 198
- Page 45: Shive, S., and T. Shumway, 2006, Is
- Page 49 and 50: Table IVOption Elasticities for AIG