EQUITY PORTFOLIO INSURANCE USING SYNTHETIC PUT OPTIONS CREATED FROM INDEX FUTURES IMPLEMENTATION PROCEDURE

BRIEF EXPLANATION OF THE SYNTHETIC OPTION CREATION MODEL

1. The term hedging and hedge re-balancing is used in this section to refer to the effect of the synthetic protective put option in hedging the value of the portfolio. Delta-matching refers to the creation of the synthetic put option by matching its delta. We make use of programming-like variables where necessary to deliver both meaning and the mathematical operations on variables.
2. At times of hedge re-balancing t0, t1, t2, t3,.... the respective values of a portfolio consisting of a long position in a put option P(i) and a long position in an equity share S(i), where i is a time-step-index are S(0) + P(0), S(1) + P(1), S(2) + P(2), S(3) + P(3),....
3. The corresponding first-order derivatives of portfolio values with respect to share price are 1 + Delta(0), 1 + Delta(1), 1 + Delta(2), 1 + Delta(3),.... where Delta(i) is the first-order derivative of the put option price with respect to the share price at time-step indexed i.
4. The equivalent share price positions are S(0) + Delta(0)*S(0), S(1) + Delta(1)*S(1), S(2) + Delta(2)*S(2), S(3) + Delta(3)*S(3),....S(i-1) + Delta(i-1)*S(i-1), S(i) + Delta(i)*S(i),.... The equivalence here, means that the first-order derivatives with respect to the share price yield same results.
5. At time-step indexed i, just before the hedge is re-balanced, the value of the portfolio is S(i) + Delta(i-1)*S(i). Re-balancing is an action to match the delta of the position so that S(i) + Delta(i)*S(i) = S(i) + Delta(i-1)*S(i) + Delta(i)*S(i) - Delta(i-1)*S(i) = S(i) + Delta(i-1)*S(i) + S(i)*(Delta(i)-Delta(i-1)). So we are essentially adjusting the position by adding S(i)*(Delta(i)-Delta(i-1)) which will result in either selling or re-purchasing of equity shares depending on whether the current delta value is greater than or less than the previous one.
6. The use of index futures to delta-match the synthetic put option is achieved by first calculating the strike price of the index put option at time of initial hedge creation as follows: protectionPutStrike = (1.0 + ((portfolioDividendYield*protectionPeriod - protectedMinimumThresholdReductionInPortfolioValue - riskFreeRate*protectionPeriod)/Beta + riskFreeRate*protectionPeriod - indexDividendYield*protectionPeriod))*currentIndexValue.
7. The protection put strike price is used to calculate the delta of the put option at subsequent time steps in the usual manner. If the calculated value of delta of the put option is D, delta-matching is achieved by D = Multiplier*Exp((riskFreeRateAtExpiryOfFuturesContract - indexDividendYield)*futuresContractExpiryPeriod).
8. Multiplier = D*Exp(-(riskFreeRateAtExpiryOfFuturesContract - indexDividendYield)*futuresContractExpiryPeriod)
9. The initial number of futures contracts used in synthetic put option creation is calculated as N = Multiplier*PortfolioValue/(IndexValue*IndexMultiplierFactor). Re-balancing at subsequent time-steps is done similarly.
10. Follow the view-by-view instructions below to implement equity portfolio insurance.

Financial solutions home page

1. Log into your account or if you are a new user, register your account and enable two factor authentication.
2. Click on the [Equity portfolio insurance-SPOIF] button, this will take you to the Dynamic-text-blocks parameters page.

Dynamic text-blocks parameters page

1. Select to create a new hedging strategy or rebalance an existing hedging strategy using synthetic put options.
2. Click the submit button, and this will take you to the Equity portfolio insurance using synthetic put options created from index futures parameters page.

Equity portfolio insurance using synthetic put options created from index futures parameters page

1. Enter the name of the underlying futures index used to calculate delta-matching parameters for the synthetic put option.
2. Select the name of currency of valuation from the drop-down list.
3. If prompted enter the portfolio value at the time the hedge was initially created. This applies when re-balancing an existing hedge created sometime ago and is necessary for record-keeping.
4. Enter the current value of the portfolio being hedged.
5. If prompted enter the index value at the time the hedge was initially created. This applies when re-balancing an existing hedge created sometime ago and is necessary for record-keeping.
6. Enter the current value of the index.
7. If prompted enter number of outstanding short index futures contracts at last hedge re-balancing time. This applies when re-balancing an existing hedge created sometime ago and is necessary for record-keeping.
8. Enter futures contract index multiplier factor. For example if it is 250 times the index, enter 250.
9. Enter futures contract expiry period.
10. Enter the beta of the portfolio being hedged. The beta of the portfolio here is strictly speaking its beta with respect to the underlying futures index. It is calculated as Beta = Covarince(PortfolioReturns,IndexReturns)/VarianceOfIndexReturns. This should not be confused with beta of the equity portfolio with respect to the market portfolio. The two are practically the same if the index is well diversified and mirrors the market portfolio. The reason for mentioning this is that, the system calculates the volatility of the equity portfolio by multiplying the beta value and the implied index volatility. If one enters the beta of the portfolio with respect to the market portfolio instead of with respect to the index when the index does not mirror the market portfolio, the results will be incorrect/inconsistent.
11. If prompted, enter the minimum percentage reduction in current value of equity portfolio for which protection is sought. This applies when creating a new hedging strategy.
12. If prompted, enter the seeded delta of the put option at last hedge re-balancing time. This applies when re-balancing an existing hedge created sometime ago.
13. Enter the annualised implied volatility of the index.
14. Enter the continuously compounded portfolio dividend yield.
15. Enter the continuously compounded index dividend yield.
16. If prompted enter the put option strike price calculated at time of initial creation of the hedge.This applies when re-balancing an existing hedge created sometime ago.
17. Enter the protection period, that is, the expiry period of the synthetic put option.
18. Enter the continuously compounded zero rate for the protection period.
19. Enter the continuously compounded zero rate for the futures contract expiry period.
20. Click the submit button and this will take you to the output display page.

Output display page

1. You can view pricing model output together with input parameters you entered.
2. At the bottom of the page you can click on the button to create database record for the current model output. This will take you to the create database record page where you should click on the create button to create the database record.
3. After clicking on the create button to create the database record, you will be taken to the database records view page, where you can scroll vertically or horizontally to view database records including the one you just created.
4. You can filter database records according to the currency of valuation using the filter box. You can click on the details link on the extreme right of a particular database record, this will take you to the particular database record details page.