Designing Allweather Overlays - Monash

BNP Paribas Quant Forum

Melbourne 2019

Designing Allweather Overlays

A study on option based systematic strategies

I. Guo and G. Loeper

Systematic strategies on options

Building blocks: Cumulative profit of selling every day the same option

• given maturity (ex 21bd)

• given strike (relative to the current spot level)

• given notional: an amount in currency, i.e. N(S(T)/S(t)-K)+

• Options are held until maturity

• Not delta hedged

• Mostly unlisted maturities (OTC)

• The price is computed by interpolating implied volatilities of listed maturities

• Input price: daily settlement prices (provided by the exchange)

• Typical strategies:

• long index (SPX)

• short OTM call

• long OTM put

• Underlying: S&P 500

• Option strikes and types: 80p, 85p, 90p, 95p, 100p, 100c, 101c, 102c, 102.5c, 103c, 104c, 105c, 110c, 120c

• Option maturities: 15bd, 21bd, 42bd, 63bd, 84bd, 126bd, 189bd, 252bd

• Options are held until maturity, no delta hedge

In the following plots, each strategy is normalized by the 1-day 99% VaR.

Systematic strategies on options

The Benchmark

BNPIFUS index is constructed by rolling the shortest maturity future contract on the S&P 500

The Benchmark is constructed as the aggregate daily relative return of the BNPIFUS index

The Benchmark has a constant $ exposure (no compounding) to be consistent with the options strategies

Compounding can be implemented after combining strategies

Selling OTM calls

Selling OTM puts

Exercise Probabilities

100c 101c 102c 103c 104c 105c 110c 115c 120c

1 15bd 0.6237 0.4893 0.3360 0.1977 0.1100 0.0627 0.0073 0.0020 0.0003

2 21bd 0.6373 0.5317 0.3971 0.2766 0.1677 0.0989 0.0127 0.0023 0.0010

3 42bd 0.6650 0.5903 0.4860 0.4067 0.3202 0.2385 0.0357 0.0077 0.0030

4 63bd 0.6921 0.6386 0.5799 0.5054 0.4251 0.3388 0.0776 0.0176 0.0047

5 84bd 0.7066 0.6537 0.5977 0.5401 0.4780 0.4159 0.1481 0.0430 0.0147

6 126bd 0.7272 0.6996 0.6691 0.6296 0.5801 0.5286 0.2336 0.0935 0.0481

7 189bd 0.7403 0.7233 0.7021 0.6829 0.6628 0.6362 0.4441 0.2042 0.0824

8 252bd 0.7687 0.7474 0.7282 0.7021 0.6851 0.6649 0.5632 0.3467 0.1719

Exercise Probability

100p 99p 98p 97p 96p 95p 90p 85p 80p

1 15bd 0.3763 0.2740 0.1967 0.1450 0.1040 0.0760 0.0167 0.0070 0.0027

2 21bd 0.3627 0.2806 0.2204 0.1713 0.1326 0.0989 0.0224 0.0104 0.0043

3 42bd 0.3350 0.2721 0.2324 0.1941 0.1628 0.1342 0.0424 0.0185 0.0158

4 63bd 0.3079 0.2683 0.2304 0.2060 0.1806 0.1575 0.0640 0.0285 0.0207

5 84bd 0.2934 0.2590 0.2228 0.1924 0.1733 0.1498 0.0795 0.0396 0.0328

6 126bd 0.2728 0.2503 0.2309 0.2080 0.1841 0.1616 0.0855 0.0481 0.0440

7 189bd 0.2597 0.2420 0.2205 0.2042 0.1872 0.1706 0.1189 0.0853 0.0690

8 252bd 0.2313 0.2121 0.1929 0.1802 0.1734 0.1640 0.1194 0.1013 0.0865

Rebalancing/Compounding

So far, the strategies presented are not compounded. We examine a few different methods of compounding

• rebalancing periodically (252bd, 63bd or 1bd);

• rebalancing whenever the value of the strategy deviates by a certain percentage (20% or 10%).

• Example covered call [Benchmark] + [103c,15bd].

Covered call with downside protection: [Benchmark] + [103c,15bd] - [100p,126bd].

Naturally, compounding leads to higher performance in favorable market conditions. However, the differences between

various compounding methods are not large. Going forward, we will simply rebalance every day whenever

compounding is considered.

Rebalancing/Compounding

Covered-calls with downside protection

Typical strategy:

long the index,

short a call option

long a put option.

Since our building block strategies involves selling options everyday, we look for

Strategy = Benchmark + aC − bP

where

• a, b ∈ 0,0.25,0.5,0.75,1

• C is a strategy that sells an out-of-the-money, short to medium maturity call option everyday

• P is a strategy that sells an out-of-the-money, medium to long maturity put option everyday

We rank strategies according to their non-compounded performance divided by the 1-day 99% VaR.

A variety of other metrics are also displayed.

Overall Results

Perf(NC)/VaR99_1

Perf(C) Perf(NC) SR(C) SR(NC) Alpha Beta VaR99_1 VaR95_1 VaR99_21 VaR95_21 Std

[102.5c,15bd]*1+[90p,189bd]*-1+[Bench]*1 44.099 1.175 0.83735 0.97991 0.69834 0.023517 0.85749 0.018988 0.011268 0.058344 0.046629 0.0063163

[103c,15bd]*1+[90p,189bd]*-1+[Bench]*1 44.002 1.2062 0.85634 0.96851 0.68761 0.022601 0.86753 0.019462 0.011666 0.060843 0.047418 0.0065605

[103c,15bd]*1+[95p,252bd]*-1+[Bench]*1 43.918 1.0646 0.77665 0.95869 0.69941 0.024135 0.83441 0.017684 0.010331 0.054495 0.037694 0.0058496

[102.5c,15bd]*1+[95p,252bd]*-1+[Bench]*1 43.863 1.0337 0.75766 0.96837 0.70979 0.025154 0.81908 0.017273 0.0099055 0.052221 0.036555 0.0056231

[103c,15bd]*1+[90p,252bd]*-1+[Bench]*1 43.666 1.2004 0.85301 0.96903 0.68862 0.022711 0.86558 0.019535 0.011359 0.059836 0.04447 0.0065254

[102.5c,15bd]*1+[95p,189bd]*-1+[Bench]*1 43.653 1.0085 0.74334 0.96351 0.7102 0.025321 0.81317 0.017028 0.009846 0.053311 0.036911 0.0055136

[103c,15bd]*1+[95p,189bd]*-1+[Bench]*1 43.492 1.039 0.76234 0.95304 0.69925 0.024263 0.82861 0.017528 0.010219 0.055585 0.0376 0.005743

[102.5c,15bd]*1+[90p,252bd]*-1+[Bench]*1 43.399 1.169 0.83401 0.97959 0.6989 0.023618 0.85473 0.019217 0.011162 0.057562 0.042581 0.0062862

[102c,15bd]*1+[95p,252bd]*-1+[Bench]*1 43.364 0.97438 0.72384 0.95613 0.71028 0.025619 0.80093 0.016692 0.0094657 0.050666 0.0348 0.0053684

[103c,15bd]*1+[100p,189bd]*-1+[Bench]*1 43.326 0.84221 0.64686 0.91039 0.69922 0.025713 0.7678 0.01493 0.0082311 0.04854 0.030614 0.0048733

[103c,15bd]*1+[100p,252bd]*-1+[Bench]*1 43.238 0.90912 0.6859 0.9398 0.70904 0.025848 0.78806 0.015863 0.0086744 0.046613 0.030874 0.0050959

Efficient frontier

Scatter plots of the performance vs. VaR.

Blue line “Capital market line”

Benchmark = black dot

Efficient frontier

Efficient frontier

Top Performers

Compounded performance without any scaling.

Compounded performance scaled by the 1-day 99% VaR. (=1+(S(T)/S(0)-1)/Var)

Top Performers

Non-compounded performance scaled by the 1-day 99% VaR.

The performance here is equivalent to our ranking metric.

Top Performers

Return histograms

Other VaRs: 21-day 99% VaR

Repeat the coloured scatter plots with variations in VaR choices.

The results are still similar to the 1-day 99% VaR case.

1-day 95% VaR

21-days 95% VaR

Without GFC

Same exercise but starting in 2010 and thus excluding the GFC.

In these market conditions, it is preferable to buy little or no downside protection.

Perf(NC)/VaR99_1

Perf(C) Perf(NC) SR(C) SR(NC) Alpha Beta VaR99_1 VaR95_1 VaR99_21

VaR95_21 Std

[103c,15bd]*1+[100p,126bd]*-0.25+[Bench]*1 41.873 1.2275 0.85824 1.2141 0.84886 0.0062729 0.9821 0.020496 0.012169 0.064947 0.038674 0.0071096

[103c,15bd]*1+[100p,189bd]*-0.25+[Bench]*1 41.784 1.2442 0.86681 1.2189 0.84916 0.0063009 0.98192 0.020745 0.012273 0.066053 0.039526 0.0071781

[104c,21bd]*1+[90p,252bd]*-0.25+[Bench]*1 41.603 1.3868 0.94053 1.2365 0.83857 0.0053123 0.98861 0.022607 0.013442 0.072172 0.046739 0.0078869

[103c,15bd]*1+[95p,63bd]*-0.25+[Bench]*1 41.48 1.3105 0.90096 1.2319 0.84694 0.0059982 0.9853 0.02172 0.012825 0.067502 0.043226 0.0074805

[103c,15bd]*1+[95p,126bd]*-0.25+[Bench]*1 41.454 1.3019 0.89662 1.2298 0.84694 0.0060641 0.98393 0.021629 0.012723 0.067887 0.041332 0.0074444

[103c,15bd]*1+[100p,84bd]*-0.25+[Bench]*1 41.422 1.2103 0.84961 1.2063 0.84677 0.006104 0.98288 0.020511 0.011915 0.063668 0.039091 0.0070555

[103c,15bd]*1+[95p,84bd]*-0.25+[Bench]*1 41.415 1.3028 0.89726 1.228 0.84573 0.0059595 0.98453 0.021665 0.012821 0.067885 0.042533 0.0074603

[104c,15bd]*1+[100p,63bd]*0+[Bench]*1 41.402 1.5932 1.0369 1.3022 0.84749 0.0056557 0.99316 0.025045 0.014312 0.07628 0.051121 0.0086036

[103c,15bd]*1+[95p,252bd]*-0.25+[Bench]*1 41.38 1.3136 0.90246 1.2335 0.84739 0.0060732 0.98433 0.021809 0.012585 0.067825 0.042306 0.0074889

[104c,21bd]*1+[85p,252bd]*-0.25+[Bench]*1 41.35 1.4293 0.96078 1.2516 0.84133 0.0054557 0.98924 0.023235 0.013741 0.073089 0.047503 0.0080303

[104c,21bd]*1+[95p,252bd]*-0.25+[Bench]*1 41.327 1.3346 0.91507 1.219 0.83585 0.0051835 0.98772 0.022142 0.013166 0.070957 0.045783 0.0076984

Efficient frontier without GFC

Covered Call Performance Contours across maturities

Strategies of the form 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 + 𝑥, 102.5𝑐 − 𝑦, 90𝑝 , with 𝑥 and 𝑦 varying across a range of maturities.

A contour of the Perf/VaR ratio is given below.

Strategies of the form 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 + 𝑥, 15𝑏𝑑 − [𝑦, 189𝑏𝑑], where 𝑥 is a call and 𝑦 is a put, varying across a range of out-of-the-money strikes. Contour of the Perf/VaR ratio.

Covered Call Performance Contours across strikes

Put vs. Put Spread vs. Put Ratio

Instead of buying a put for downside protection, one could also consider replacing it with a put spread or a put ratio. We effectively exchange some performance (via lower premia) with risk (less downside protection).

Covered-calls with put spread

Buying 100p, 95p or 90p while selling the 85p of the same maturity at the same quantity.

Perf(NC)/VaR99_1


[102.5c,15bd]*1+([100p,63bd]-[85p,63bd])*-0.75+[Bench]*1

36.977 0.97607 0.7578 0.72084 0.55964 0.012811 0.94003 0.020494 0.010376 0.06472 0.037982 0.007133

[102.5c,15bd]*1+([100p,63bd]-[85p,63bd])*-1+[Bench]*1

36.671 0.81737 0.65694 0.68468 0.55029 0.013185 0.89969 0.017914 0.0086946 0.051927 0.029028 0.0062887

[102.5c,15bd]*1+([95p,63bd]-[85p,63bd])*-1+[Bench]*1

36.621 1.0871 0.82653 0.7383 0.56133 0.012631 0.952 0.02257 0.012033 0.067347 0.04956 0.0077566

[103c,15bd]*1+([100p,63bd]-[85p,63bd])*-0.75+[Bench]*1

36.377 1.0039 0.77679 0.71838 0.55585 0.012377 0.94822 0.021354 0.010802 0.065676 0.038944 0.0073616

[103c,15bd]*1+([100p,63bd]-[85p,63bd])*-1+[Bench]*1

36.126 0.84463 0.67593 0.68433 0.54765 0.012712 0.91254 0.01871 0.0091724 0.052883 0.030542 0.0065017

[102c,15bd]*1+([100p,63bd]-[85p,63bd])*-0.75+[Bench]*1

36.091 0.92046 0.72398 0.70438 0.55402 0.012706 0.9296 0.02006 0.010034 0.063747 0.036311 0.0068837

[103c,15bd]*1+([95p,63bd]-[85p,63bd])*-1+[Bench]*1

36.019 1.1149 0.84553 0.73426 0.55684 0.012216 0.95758 0.023474 0.012335 0.069947 0.050788 0.0079988

[102c,15bd]*1+([100p,63bd]-[85p,63bd])*-1+[Bench]*1

35.905 0.76445 0.62312 0.66459 0.54172 0.013037 0.88323 0.017354 0.0082534 0.050954 0.027482 0.0060593

[102c,15bd]*1+([95p,63bd]-[85p,63bd])*-1+[Bench]*1

35.556 1.0302 0.79271 0.72465 0.55761 0.01256 0.94517 0.022295 0.011664 0.064502 0.048108 0.0074888

[104c,15bd]*1+([100p,63bd]-[85p,63bd])*-1+[Bench]*1

35.303 0.83672 0.67881 0.64269 0.52139 0.010623 0.93075 0.019228 0.0095956 0.054571 0.033069 0.0068582

[102.5c,15bd]*1+([100p,84bd]-[85p,84bd])*-0.75+[Bench]*1

35.272 0.9884 0.7699 0.7036 0.54806 0.012015 0.94281 0.021828 0.010763 0.069888 0.043307 0.0074001

10085

Perf(NC)/VaR99_1


[102.5c,15bd]*1+([100p,63bd]-[85p,63bd]*[100p,63bd,stri]/85)*-1+[Bench]*1 36.252 0.86336 0.69193 0.669 0.53616 0.012255 0.90134 0.019087 0.009001 0.0617 0.029473 0.0067982

[103c,15bd]*1+([100p,63bd]-[85p,63bd]*[100p,63bd,stri]/85)*-1+[Bench]*1 36.14 0.89086 0.71093 0.66974 0.53447 0.011852 0.91376 0.019672 0.0094445 0.062656 0.031217 0.007007

[102.5c,15bd]*1+([95p,63bd]-[85p,63bd]*[95p,63bd,stri]/85)*-1+[Bench]*1 35.887 1.1203 0.84986 0.73098 0.55451 0.012168 0.9534 0.023681 0.012381 0.070056 0.050136 0.0080736

[102.5c,15bd]*1+([100p,63bd]-[85p,63bd]*[100p,63bd,stri]/85)*-0.75+[Bench]*1 35.811 1.0119 0.78405 0.70975 0.54995 0.012207 0.93973 0.021894 0.01072 0.07205 0.038517 0.0075101

[103c,15bd]*1+([100p,63bd]-[85p,63bd]*[100p,63bd,stri]/85)*-0.75+[Bench]*1 35.599 1.0399 0.80304 0.70816 0.54688 0.011818 0.94796 0.022558 0.011025 0.073006 0.039346 0.0077352



[102.5c,15bd]*1+([100p,84bd]-[85p,84bd]*[100p,84bd,stri]/85)*-0.75+[Bench]*1 35.274 1.0181 0.79411 0.68671 0.53562 0.011209 0.94374 0.022513 0.011066 0.078074 0.043916 0.00781




Covered-calls with put ratio

Buying put with strike x while selling the 85p of the same maturity at the quantity of x/85.

10085

Top Strategies: Compounded no scaling

Top Strategies: Compounded scaled by 1 day 99% Var

Top Strategies: Non compounded scaled by 1 day 99% Var

Sensitivity Regression

We will regress the top covered call strategy, 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 + 102.5𝑐, 15𝑏𝑑 − [90𝑝, 189𝑏𝑑],

against the Benchmark and the implied volatility to estimate contributions form various sensitivities.

Put Strike vs. Put Weight

We examine the effect of buying puts for downside protection, and whether there are any equivalences

between different values of put strikes and put weights.

Combining with index

First, let us look at the case of buying puts along with the Benchmark, and compare the effect this has on the

1-day 99% VaR as well as the Perf/VaR ratio.

Perf(NC)/VaR99_1


[85p,126bd]*-1+[Bench]*1 27.105 0.81078 0.72164 0.46395 0.41294 0.002934 0.96671 0.026624 0.016225 0.08612 0.059735 0.0092059

[80p,126bd]*-1+[Bench]*1 26.99 0.88057 0.77826 0.47053 0.41586 0.0029034 0.9757 0.028835 0.017255 0.099332 0.065252 0.0098584

[85p,126bd]*-0.8+[Bench]*1 26.825 0.84006 0.75322 0.45391 0.40699 0.0022164 0.98107 0.028079 0.01696 0.094302 0.064512 0.0097492

[90p,126bd]*-1+[Bench]*1 26.573 0.68346 0.62576 0.43174 0.39529 0.0020933 0.95536 0.023549 0.014838 0.075127 0.05582 0.0083391

[95p,126bd]*-1+[Bench]*1 26.236 0.54189 0.51261 0.3929 0.37168 0.00096585 0.94028 0.019539 0.012524 0.064164 0.048636 0.0072653

[80p,126bd]*-0.8+[Bench]*1 26.22 0.89421 0.79851 0.45791 0.4089 0.0022259 0.98572 0.030454 0.017715 0.10487 0.071777 0.010287

[90p,126bd]*-0.8+[Bench]*1 26.036 0.739 0.67651 0.43078 0.39435 0.0015454 0.97585 0.025983 0.015805 0.081087 0.059332 0.0090368

[95p,126bd]*-0.8+[Bench]*1 25.96 0.62533 0.58599 0.40396 0.37855 0.00068842 0.97004 0.022573 0.013747 0.069581 0.054401 0.0081546

[90p,126bd]*-0.6+[Bench]*1 25.394 0.79115 0.72726 0.42597 0.39157 0.0010705 0.98839 0.02864 0.016691 0.092573 0.066346 0.0097838

[85p,126bd]*-0.6+[Bench]*1 25.389 0.86607 0.78479 0.44173 0.40028 0.0015691 0.99047 0.030911 0.017627 0.10248 0.072953 0.010328

[80p,126bd]*-0.6+[Bench]*1 25.125 0.90533 0.81876 0.444 0.40154 0.0015989 0.99258 0.032588 0.018161 0.11041 0.079022 0.010741

Combining with covered call

Next, let us look at the case of buying puts along with selling a covered-call, and compare the effect

this has on the 1-day 99% VaR as well as the Perf/VaR ratio.

Perf(NC)/VaR99_1


[100p,126bd]*-1+[102.5c,15bd]*1+[Bench]*1 42.932 0.71216 0.56761 0.84392 0.67263 0.025241 0.71739 0.013221 0.0073713 0.041561 0.028741 0.0044453

[90p,126bd]*-1+[102.5c,15bd]*1+[Bench]*1 41.526 1.1039 0.80663 0.9021 0.65917 0.020823 0.86697 0.019425 0.011575 0.06021 0.048206 0.0064463

[95p,126bd]*-1+[102.5c,15bd]*1+[Bench]*1 41.495 0.91195 0.69349 0.87694 0.66686 0.022598 0.81293 0.016713 0.0098166 0.052395 0.037054 0.0054781

[100p,126bd]*-0.8+[102.5c,15bd]*1+[Bench]*1 41.235 0.86589 0.66617 0.86076 0.66222 0.021347 0.85309 0.016156 0.0091588 0.04832 0.033264 0.0052992

[95p,126bd]*-0.8+[102.5c,15bd]*1+[Bench]*1 41.029 1.0307 0.76687 0.87296 0.64949 0.019677 0.88944 0.018691 0.011041 0.057077 0.043795 0.0062198

[85p,126bd]*-1+[102.5c,15bd]*1+[Bench]*1 40.818 1.2776 0.90252 0.9289 0.6562 0.019846 0.90008 0.022111 0.012817 0.069286 0.052763 0.0072452

[90p,126bd]*-0.8+[102.5c,15bd]*1+[Bench]*1 39.928 1.1864 0.85738 0.88666 0.64076 0.018548 0.91371 0.021473 0.012256 0.06561 0.050926 0.0070487

[85p,126bd]*-0.8+[102.5c,15bd]*1+[Bench]*1 39.596 1.3254 0.93409 0.90397 0.6371 0.017917 0.93048 0.023591 0.01358 0.07381 0.054422 0.0077234

[80p,126bd]*-1+[102.5c,15bd]*1+[Bench]*1 39.494 1.3772 0.95913 0.92433 0.64373 0.018525 0.92251 0.024286 0.013866 0.07884 0.055736 0.0078489

[100p,126bd]*-0.6+[102.5c,15bd]*1+[Bench]*1 39.046 1.0211 0.76472 0.84607 0.63362 0.017936 0.92051 0.019585 0.010796 0.055906 0.040033 0.0063577

[95p,126bd]*-0.6+[102.5c,15bd]*1+[Bench]*1 38.63 1.1477 0.84025 0.85352 0.62486 0.01708 0.93326 0.021751 0.012031 0.062474 0.048846 0.0070836

OTC vs. Listed

Single strategies

Fixing the strike at 102.5c, let us compare the listed 3fripb and 1m3fripb calls with nearby otc calls. Everything is scaled by their respective VaR.

Similarly let us compare 90p with longer maturities.

OTC vs. Listed

OTC vs. Listed

maturity

OTC vs. Listed

Stability of the vega

OTC vs. Listed

Stability of the delta

OTC vs. Listed

Single strategies

Zooming on 2008

Listed covered calls with downside protection

Recall that the top performing OTC strategies had a Perf/VaR ratio of 44.

As shown below, the top performing Listed strategies have a ratio of 36.

Perf(NC)/VaR99_1


[105c,1m,3fri,pb]*1+[90p,9m,semester,3fri,pb]*-1+[Bench]*1 36.654 0.86689 0.69011 0.69172 0.55067 0.014734 0.83576 0.018828 0.011404 0.061476 0.043625 0.0066018











Top listed covered call vs. Top OTC covered call

Let us plot the top listed covered call strategy against the top OTC covered call strategy.

First, we plot the compounded performance without any scaling.

Compounded performance scaled by the 1-day 99% VaR

Non-Compounded performance scaled by the 1-day 99% VaR

Selling options vs. running delta hedge only

Single strategies

First example is [105c, 21bd].

Instead of buying/selling options, another possibility is to run the corresponding delta hedge portfolio. The

difference would mainly come from the difference between the implied vs. realized volatilities.

Next example is [95p,126bd].

Selling options vs. running delta hedge only

Covered calls

We can combine the two for a covered call. Since the options are usually more expensive than the delta hedge, we can also try using a true call but protected by a delta hedge only put.

Conclusions

• Flexible tool to look at a range of possibilities

• For this type of strategies (long index short call long put) better to chose:

• Short maturity slightly otm call

• Longer maturity (6m-1y) close to atm or slightly otm put

• Non-listed maturities (i.e. one expiry every day) allow to benefit more from the short maturity premium

• Ways to cheapen the hedge (put spread, put ratio), but VaR increases

• Efficient frontier analysis shows the benefit of adding options to the portfolio

• Conclusions will always depend on the choice of the performance metric

Designing Allweather Overlays - Monash

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