How active fund managers can extract value from the derivatives market and why the returns available aren’t too good to be true Monte Carlo simulations

What is a Monte Carlo simulation? Calculation that is dependent on a repeated random sample Calculation – determine the of value of equity options Random sample – movement of underlying market through time Time Underlying market Count the number of points for each outcome to calculate the probabilities

Can we impose our own views on the Monte Carlo simulation? Drift – general movement of the underlying in a particular direction Shock – volatility of the movement Time Underlying market Drift Volatility Overlay an investor view of drift and volatility to generate a series of outcomes and hence probabilities

In 1873, Joseph Jagger used his background as an engineer to predict the outcome of the Monte Carlo roulette wheels which at the time exhibited mechanical imbalances He won a total of $325,000 over several days, equivalent to around £10mm today

What do the Monte Carlo simulation results look like? Investor assumptionsMarket parameter assumptions -Investor assumptions are from DB analyst Jim Reid -Market parameter assumptions include implied volatility, dividends, interest rates -6 year time to maturity -Market parameters imply a 17% probability that underlying market will fall by 70% or more – quite surprising! Underlying marketProbabilityUnderlying marketProbability < -70%17.36%< -70%0.22% -70%5.00%-70%0.95% -60%5.13%-60%2.32% -50%4.74%-50%4.08% -40%5.71%-40%5.52% -30%5.66%-30%6.74% -20%5.91%-20%7.35% -10%6.47%-10%7.54% 0%6.10%0%7.47% 10%6.49%10%7.01% 20%5.74%20%6.49% 30%5.27%30%5.86% 40%4.91%40%5.27% 50%3.93%50%4.61% 60%3.47%60%4.10% 70%2.10%70%3.47% 80%1.95%80%3.08% 90%1.17%90%2.56% 100%0.81%100%2.25% 110%0.63%110%1.90% 120%0.49%120%1.66% 130%0.22%130%1.39% 140%0.73%140%8.15% Total100.00%Total100.00%

Studio flat, central Monte Carlo, 3 min walk from the Casino – Guess how much? Yours for a measly £1.8mm

Use Monte Carlo results to value a vanilla ATM put option -Put price estimated by Monte Carlo analysis very close to actual option price in market -Relative to the investor’s assumptions the market price of a vanilla ATM put looks expensive! Underlying marketProbabilityPut returnExpected < -70%0.22%80.00%0.18% -70%0.95%65.00%0.62% -60%2.32%55.00%1.28% -50%4.08%45.00%1.83% -40%5.52%35.00%1.93% -30%6.74%25.00%1.68% -20%7.35%15.00%1.10% -10%7.54%5.00%0.38% Total9.00% DF90.06% MC value8.11% Underlying marketProbabilityPut returnExpected < -70%17.36%80.00%13.89% -70%5.00%65.00%3.25% -60%5.13%55.00%2.82% -50%4.74%45.00%2.13% -40%5.71%35.00%2.00% -30%5.66%25.00%1.42% -20%5.91%15.00%0.89% -10%6.47%5.00%0.32% Total26.72% DF90.06% MC value24.06% Actual option price25.80% Market parameter assumptionsInvestor assumptions

Use Monte Carlo results to value an ATM put with knock-in at 60% -Put price estimated by Monte Carlo analysis very close to actual option price in market -Relative to the investor’s assumptions the market price of a vanilla ATM put looks expensive! Underlying marketProbabilityPut returnExpected < -70%0.22%80.00%0.18% -70%0.95%65.00%0.62% -60%2.32%55.00%1.28% -50%4.08%45.00%1.83% -40%5.52%0.00% -30%6.74%0.00% -20%7.35%0.00% -10%7.54%0.00% Total3.91% DF90.06% MC value3.52% Underlying marketProbabilityPut returnExpected < -70%17.36%80.00%13.89% -70%5.00%65.00%3.25% -60%5.13%55.00%2.82% -50%4.74%45.00%2.13% -40%5.71%0.00% -30%5.66%0.00% -20%5.91%0.00% -10%6.47%0.00% Total22.09% DF90.06% MC value19.90% Actual option price21.35% Market parameter assumptionsInvestor assumptions

Graphical representation of the two different outputs

Underlying marketProbabilityDigital returnExpected 20%17.36%20.00%3.47% 35%5.00%35.00%1.75% 45%5.13%45.00%2.31% 55%4.74%55.00%2.60% 65%5.71%150.00%8.57% 75%5.66%150.00%8.50% 85%5.91%150.00%8.86% 95%6.47%150.00%9.70% 105%6.10%150.00%9.16% 115%6.49%150.00%9.74% 125%5.74%150.00%8.61% 135%5.27%150.00%7.91% 145%4.91%150.00%7.36% 155%3.93%150.00%5.90% 165%3.47%150.00%5.20% 175%2.10%150.00%3.15% 185%1.95%150.00%2.93% 195%1.17%150.00%1.76% 205%0.81%150.00%1.21% 215%0.63%150.00%0.95% 225%0.49%150.00%0.73% 235%0.22%150.00%0.33% 245%0.73%150.00%1.10% Total111.80% DF90.06% Bank Value100.68% -Using market parameters the “value” of the investment is close to 100%, as expected. -Relative to the investor view this represents a 28% undervaluation! Time to price a digital structure -Pays 150% if underlying is above knock-in level at maturity -Knock-in put level at 60% -6 year time to maturity Market parameter assumptions Investor assumptions Underlying marketProbabilityDigital returnExpected 20%0.22%20.00%0.04% 35%0.95%35.00%0.33% 45%2.32%45.00%1.04% 55%4.08%55.00%2.24% 65%5.52%150.00%8.28% 75%6.74%150.00%10.11% 85%7.35%150.00%11.02% 95%7.54%150.00%11.32% 105%7.47%150.00%11.21% 115%7.01%150.00%10.51% 125%6.49%150.00%9.74% 135%5.86%150.00%8.79% 145%5.27%150.00%7.91% 155%4.61%150.00%6.92% 165%4.10%150.00%6.15% 175%3.47%150.00%5.20% 185%3.08%150.00%4.61% 195%2.56%150.00%3.85% 205%2.25%150.00%3.37% 215%1.90%150.00%2.86% 225%1.66%150.00%2.49% 235%1.39%150.00%2.09% 245%8.15%150.00%12.23% Total142.31% DF90.06% Investor Value128.17%

Graphical representation of the two different digital outputs - Digital nature of structure produces spike in the return - Higher digital return probability for Jim Reid assumptions - Redistribution of probabilities for lower returns

Conclusions - You can extract value if your market view differs from the “view” implied by the derivatives market - Distortions in the market exists due to supply and demand (dumb money versus smart money) - Structured investments can offer boringly-predictable outcomes Next time – fitting structured investments into your overall asset allocations?