Structured Products
Corporate Equity Derivatives
“Complexity can be dangerous if it inhibits a genuine understanding, and an accurate calculation, of risks and exposure,” said Colombo, a former Morgan Stanley counsel. “On the other hand, a complex arrangement may present a very lucrative opportunity that ought not to be passed up1.”
Equity Collar Trades
A collar trade provides investors a way to borrow money using equity shares as collateral while hedging against a decline in stock prices. The borrowing optically looks risk-free however is not immune to default and the resulting market exposure.
• In February, 2018, Geely, a Hangzhou-based automotive company bought a $9 billion stake in Daimler AG using the biggest collar of its kind, Bloomberg has reported.
• In 2016, Steinhoff International Holdings borrowed $1.5 billion from a group of lenders through a margin loan pledging stock in the company as collateral without a collar. The deal went bad. Over 2 days in December, Steinhoff’s shares plunged 80%. Global investment banks lost more than $1B2.
• The collar transaction can be very lucrative. When Chinese billionaire Li Shufu needed help in building a 10% stake in Daimler, Bank of America, Merrill Lynch, and Morgan Stanley made around $250m in upfront profits for providing Mr. Li with a “funded equity collar”.3.
How a Collar Works
In this example, a $2M 2 year loan is taken out at a discount from the share value. Using an 80% discount, the amount of shares pledged is $2.5M. The loan is 1.5% above Libor, lower than available on a non-collateralized loan for this borrower. AAPL shares are used as the example. Spot is 191.70, and a 20% out-of-the money (OTM) 153.36 put is purchased. Lower moneyness options have a higher volatility for AAPL, and a mid-point volatility of 24.3% is used. In order to make the put zero cost, a call option is sold. Since the volatility for this higher moneyness option is lower at 21%, a higher strike is achieved at 248.16. The moneyness indicates that out-of-the money puts on AAPL are priced with a higher volatility.
The number of shares put up as collateral = 2,500,000/191.70 =13,041 which also equals the number of put options and number of call options. The borrower owns the puts and has written the call. The puts are placed as collateral with the lender.
Scenario A
If spot at expiry is below the put strike, the put will be exercised automatically, the collateral shares delivered to the put holder and cash received for the value of the loan. E.g. spot is 120 the lender gets 153.36 * 13,041 = $2M.
Scenario B
If spot at expiry is above the call strike, the borrower will not default on this particular transaction since the exercise of the call, e.g. if spot is 300, the cash received by the borrower or its other creditors will be 248.16 x 13,041 = $3,236,255, more than enough to pay off the loan and any loan cancellation fee. (This amount is capped at the strike).
If spot is between the put and call strikes, for similar reasons, the borrower is not likely to default on this particular arrangement since it is more advantageous to sell the shares.
The following chart illustrates the payout possibilities. Below the put strike, the borrower exercises the put and receives $2m the value of the loan. Anywheres above that to the call cap, the borrower sells the shares with excess funds after paying off the loan. Above the call strike, the borrower delivers the shares for the agreed strike and also has an excees of funds from which the loan is paid.
Risks
Wrong-way risk
. If the borrower lends money against its own shares as collateral then the value of the collateral falls as the borrower’s credit worthiness declines. This is what happened with Steinhoff. Additionally, if the borrower writes puts on its own shares, the same risk exists.
Monitoring Risk through RiskSnap
1) FRN 2 year loan to “Corporate1” for $2M 3-Month Libor +150bp.
2) Collateral received $2.5M, 13041 shares. Lodged with a depository..
3) Collateral received 153.36 2yr Put option on 13,041 shares. (Sold by “Broker4” to “Corporate1” at zero cost. “Corporate1” places the put option as part of the collateral with the lender.
4) Call sold by “Corporate1” to “Broker” at zero cost. This has no market risk nor credit risk to the lender unless the lender is the counterparty to the call. However, this transaction is managed separately.
Risk is calculated separately for the loan.
The collateral is managed as a netted book due to the underlying assets being AAPL shares and put option and thereby posing little correlation risk.
a) The MTM of (2,574,447) represents the market value of the loan that “Corporate1” owes to the lender.
b) The value of the loan to the lender decreases as rates rise. The opposite is true for the borrower, therefore the margin on the FRN is measured using Antithetic risk. This value is determined over the 1 year period that contains the largest loss over a 10 year period. On 15 Sep 2008, 2 year rates dropped by 25 bp resulting in a historically simulated loss of $8,000 adjusted for a holding period. Although HVaR can be used, in this case the lender prefers to use tail risk or expected shortfall. Expected shortfall is calculated as $4,714. This is the margin required for the Floating Rate Note (FRN).
c) The value of the collateral is determined based on the market value of equity collateral and equity put less the value of the “hair-cut”. The market value of the put option on the trade date was $7.77. Added to spot of 191.70, 199.47 x 13,041 = $2,601,288. The haircut on this portfolio at that date was determined in RiskSnap as $324,998 and therefore the value of collateral is $2,276,292. The risk on the collateral (haircut) is the risk on the shares offset by the risk on the put option.
The equity share risk of $324,998 can be seen below where the worst case was 29-Sep-2008. On that day AAPL shares were down close to 20 % and appeared to be due to a stock ratings cut by RBC Capital and Morgan Stanley. Both were concerned about AAPL’s prices in a worsening economy.
The same magnitude of drop on the valuation day of this example would have produced a loss of close to $500,000. Assuming that liquidation was not immediate but over 2 more days of volatility (the holding period), the loss could be as high as 633,541. The protective properties of the put was limited to 193,000 since the put delta at this point was 32%. The net effect was 440,000 for this worst case. Since the average of the tail risk is used, the haircut was 324,998. If the put was not netted against the shares, the sum of the individual risks would have been 491,179. The collateral netting benefit for haircus is shown in the graph below.
d) The summary of Collateral and excess/deficit is,
• MTM of the FRN -$2,574,447
• Value of the collateral received $2,276,292
• Cash collateral $278,122 (for this example, it is assumed that the borrower has placed funds for the haircut).
• Total Equity = -$2,574,447 + $2,276,292 + $278,122 = (20,033).
• Net owed from borrower to lender: $(24,747).
Equity Linked Notes
Equity Linked Notes are pre-packaged investments that normally include assets linked to interest rates plus one or more derivatives. Examples are where the final payout on the amount invested depends on movements (positive or negative) of one or more underlying assets (equities, commodities, foreign exchange).
In some cases the principal amount is protected and in other cases the principal amount will decrease with the value of the underlying asset.
The package allows the investor to participate in wholesale pricing for interest rate products and option products not normally available in the retail market. The initial bid-offer spread allows the dealer to hedge and manage the distribution and payouts. This strategy works better in a higher interest rate environment since there is more cash for the investor to "pay" for the options and also with higher option volatility since the probability of the assets being in-the-money is higher.
RBC’s Principal Protected Canadian Large Cap Guaranteed Return Notes, Series 122, issued Nov 22, 2022 is used for the example. This note provides a guaranteed coupon 3% for 5 years, paid monthly or 0.25% per month. The return at maturity is linked to the price performance of 5 Canadian large cap shares equally weighted where the return is based on the closing price of the equities Nov 22, 2027 compared to the base price as of close Nov 21, 2022 as listed on TSX. The return is applied to 50% of the Principal. The Principal due at maturity(t) is,
Where e represents the share prices at time 0 and at maturity. The principal investment is $100,000. A hypothetical example for prices at maturity [from the prospectus] follows.
Where e1= Enbridge Inc. (ENB), e2=Manulife Financial Corporation (MFC), e3=Rogers Communications, Inc (RCI/B), e4=Sun Life Financial Inc. (SLF) and e5=TC Energy Corporation (TRP). The starting prices were the close on TXS on Nov 21st. Note that SLF had a dividend payment on Nov 22. Yahoo’s Nov 21st adjusted price is after the dividend whereas TSX’s price is before the dividend. Although the overall return in this example is 24%, the actual return is one-half that since only 50% of the Principal applies.
In this example, the last equity has a negative return which reduces the overall return. Since the return has a floor of 0, if the sum of the returns is negative then the return is zero and no lower, that is, the principal amount of $100,000 is guaranteed.
This product depends on the volatility due to the optionality that puts the floor on the maximum loss. The portfolio volatility in turn depends on the correlations between the assets. If all assets were correlated then a drop in price of one asset would impact the entire portfolio. Where assets are uncorrelated, a loss in one asset will be offset by a gain in another asset. In the case of this portfolio as of the pricing date Nov 25, 2022, the correlation matrix (with volatility in the diagonal) was as follows:
The energy related companies, Enbridge and TC Energy Corporation are highly correlated at 0.74, as are the two financials, Manulife and Sun Life at 0.64. However, the correlation between a financial (Manulife) and energy (Enbridge) while high, is not as high at 0.47. Rogers, the telecommunications company has low correlation with the others averaging about 0.34. Volatility for TC Energy Corporation, 54% as of Nov 25th is high relative to the other equities. Portfolio volatility may be measured by the general Markowitz formula with weighting as follows: Using the general Markowitz formula below, the portfolio volatility can be calculated. When all correlations = 1, the portfolio volatility is the same as the average of the volatilities, 32.5%. Reduction in correlations reduces the portfolio volatility as gains in one asset is offset by losses in another. The porfolio volatility for the above is 24%.
- Correlations cannot be hedged through the market since there are no easily obtained correlation products. Historical correlations for this examples are based on historical equity prices.
- Deltas are difficult to hedge for basket options since a change in correlation will affect more than one asset in the basket. The safest hedge for the structurer is to overhedge by buying the individual options.
- Historical correlations depend on the observation period. In this example, the number of observations is based on days to maturity with a floor of 25 business days and max of 252 business days.
- Implied volatilities have been used for the volatilities. Options traded on exchanges are generally limited in term and 5 year options are not available for the term. For the example the volatilities have been capped at the maximum term found
- The strike for the option is 1, ie. 1 x 50000 will be paid on exercise. The expected forward is the sum of the ratio of the forward/spot at inception multiplied by the weight, in this case 20%.
- The expected forward for each equity is calculated as f = s x exp((r-q)t) where r is the interest rate derived from the Canadian Treasury Curve, and q, the dividend yield is based on the latest one year’s value of dividends divided by current spot. The dividend yield can alternatively be derived using put-call parity from the volatility surface.
As of Nov 25, 2022, the bond was priced at 94,810 or a loss of -C$5,190 for a C$100,000 investment.
The value of the (basket) option was C$7,425 for a net gain of C$2,235.
Alternatively, purchase of the underlying options separately on C$50,000 was C$10,293 offering the investor a 28% savings through the basket. However, the exercise of the basket will result in losses offsetting gains, whereas individual options that expire out-of-the-money are not exercised.
Risks
- If the issuer defaults before the maturity date, there is a risk that the principal as well as interest payments and equity returns will be lost, otherwise at a minimum the principal will be returned.
- A decrease in one or more equity prices will lower the return.
- A decrease in option volatility will reduce the likelihood of exercise and will lower the price of the structure.
- A decrease in correlation will reduce the portfolio volatility resulting in a lower valuation for the structure as gains in one equity will be offset by losses in another.
- An increase in interest rates will reduce the value of the fixed payments received on the principal which is twice the amount of the principal for the equity return.
Monitoring Risk through RiskSnap
There are two transactions in the structure, the fixed interest rates at 3%, and the equity return. The risk is shown separately, then combined as the equity linked note.<;>
The interest rate risk based on an absolute movement in rates, was greatest on Mar 18th, 2020. The expected shortfall for the stress period was -$4,190 on the $100,000 5 year note
The equities benefited from the increased volatility during the same period, and the worst case risk for the equity portion alone occurred later with an expected shortfall of -$760.
When the two transactions are combined, the expected shortfall is -3,910. The main risk source for this transaction are interest rate changes where the Canadian Treasury 5 yr rate on March 18, 2020 change by 13bp, and the 2 day change from the 16 to the 18th was 32bp..
