Valuing Retail Structured Products Jos van Bommel Luxembourg School - PowerPoint PPT Presentation

Valuing Retail Structured Products Jos van Bommel Luxembourg School of Finance

What are Retail Structured Products? Of-the-shelve financial securities sold to private investors, mostly by commercial banks, traded either over the counter, or through a stock exchange. They can be classified as i) guaranteed products, ii) leverage products, and iii) others. Guaranteed products are long term (3-10 years), and offer investors a guaranteed payoff plus an upside linked to the performance of an index. They are mostly sold over the counter and unlisted. Leverage products offer accelerated participation in stocks or indices (a.o.). They are short term investments, listed on a stock market.

Retail Structured Products , raison d´être Market Completion They offer plays that are not available, or difficult to implement, for private investors. The demand for Guaranteed Products derives from loss aversion , either as a behavioral bias, or as a genuine financial constraint. The demand for Leveraged Products derives from the desire for speculation . Both motives, have, IMHO , merit. The key question is Is the product fairly priced? A follow up question would be whether they are fairly marketed …

Outline of the talk 1) Example of a Guaranteed Product. Valuation by replication Valuation by simulation 2) Example of a Leverage Product (a barrier option) Valuation in a Black Scholes world (Merton, 1977) . Valuation by simulation 3) Empirical findings on the pricing of Leverage Products

Guaranteed Products Offer a guaranteed payoff, with an upside tied to one or more stocks or stock market indices. Example of a simple GP: BNP Fonds a Capital Protégé “X2”

BNP X2 Avec X2, profitez d’une hausse à 4 ans de l’indice DJ Euro Stoxx 50 1 dans la limite de 60%, et récupérez à l’échéance, jusqu’à 150% de votre capital investi 2 . L’indice DJ EuroStoxx 50 1 , diversifié géographiquement et sectoriellement, est constitué des 50 valeurs phares de la zone euro . Le 7 avril 2014, on calcule la performance de l’indice DJ Euro Stoxx 50 par rapport à son cours d’origine 3 du 7 avril 2010. La Performance de l’Indice est alors égale à la performance ainsi calculée dans la limite de 60%, et sans pouvoir être négative (« Performance Finale de l’Indice ») A l’échéance, le 17 avril 2014, la Valeur Liquidative Finale du Fonds est égale à 90% du capital investi majoré de la Performance Finale de l’indice: elle sera donc comprise entre 90% et 150% (90% + 60%) de la Valeur Liquidative de Référence 4 , soit un rendement actuariel maximum de 10,55% 5 .

BNP X2 To make a long story short.. The payoff per €1000 investment is, after four years: X2 Payoff 1500 1000 500 -20% 0% 20% 40% 60% 4 year return on Stoxx50 Or, payoff = €900 + € max (0, min (600, r stoxx ×1000))

BNP X2 Clearly, we can replicate the payoff of the BNP X2 with X2 Payoff 1500 A Call Option on the Stoxx with X = S 1000 A 4-yr deposit of €PV(900) 500 -20% 0% 20% 40% 60% Less a Call with X = 1.6 S 4 year return on Stoxx50 We know that the value of a Call is C( S , X , ∆ t , σ , r f )

Value of the BNP X2 With ∆ T and r f (≈2%) given, the replication value of the BNP X2 depends on σ only: 990 € 980 € 970 € 960 € 950 € 940 € 930 € 920 € 910 € 900 € 0% 10% 20% 30% 40% 50% 60% 70% 80% σ , anual volatility - Option values are computed with the Black Scholes formula - At issue, the long term implied volatility of the Stoxx was about 23% - The 3 year swap rate was 1.96% , the 5 year rate was 2.46% - Assumption: BNPs credit risk is zero …

Value of the BNP X2 With ∆ T and r f (≈2%) given, the replication value of the BNP X2 depends on σ only: €990,00 €985,00 €980,00 €975,00 €970,00 €965,00 18% 20% 22% 24% 26% 28% 30% 32% 34% σ , anual volatility

Value of the BNP X2  The BNP X2 is overpriced by about 2%. (compared to the replication value ) Which, IMHO, is not unreasonable for a 4 year security. Constructing the replicating portfolio would probably cost cost much more than 2% for most retail investors: To replicate a €1000 investment in BNP X2s, you would need to trade options for approximately €275 .. ( buy €215 worth of at-the-money Calls, and sell €60 worth of X = 1.6 S Calls. )

Complex Guaranteed Products Locally Capped products are popular in the U.S. These pay a garantee, plus the sum of series of (e.g. monthly) capped returns of an underlying. Ex.: A five year contract, guarantee = 100%, with an upside computed as the sum of monthly returns, capped at 5%.  the maximum payoff is 1+60×5% = 400% the original investment. These products also come in compounded forms. If the above were a compounded product, the maximum payoff would be (1+5%) 60 = 18,679 times the investment !!!

Locally Capped Products Because their payoffs are path dependent , these products are difficult to value. Using a Monte Carlo method of Rossetto and van Bommel (2009), Bernard and Boyle (2010) show that LCPs are overpriced by 14% or more , and have expected returns < r f Marketing is very agressive, through unrealistic scenarios : Prospectuses contain approx. 7 scenarios, of which 5 or 6 are extremely unrealistic. Selling commisions to (brokers) are very high (average 6%!! ). Evidence (and theory) suggests that overpricing increases in complexity (Stoimenov and Wilkens (2007).

Excerpt from the Prospectus of the NAS.2 ( monthly compounded LCP) , issued by a Citigroup If the Nasdaq 100 would Excerpt from the prospectus of the NAS appreciate by 3% every month… Your return would be > 600% Source: Bernard et al. (2009)

Excerpt from the Prospectus of the NAS.2 (monthly compounded LCP) , issued by a Citigroup If the Nasdaq 100 would appreciate by more than 5.5% (the cap) every month… Bernard and Boyle show that the probability of this is lower than 10 -19 … Your return would be 3325%!! Source: Bernard et al. (2009)

Locally Capped Products Five additional examples are given, three of which are (also) unreasably optimistic. Representative scenarios such as +14%, -9%, +11%, -12%, etc. Are left out because these return 0, due to the capped increases and the uncapped decreases..

Complex Garanteed Products in Europe Three years, return is minimum 0% maximum 18% (AER 5.66%) For every month that Apple, Vodafone and Microsoft go up, you accumulate 0.5%

Locally Capped Products in Europe 9 year “FCP” (Fonds Commun de Placement), essentially an ETF. Value at maturity = maximum value during its life. (“Cliquet”) E.g. if after 3 months, the FCP trades at €109, you get at least €109 back at maturity. The “click” effect does not apply to a visible index or basket, but to the fund itself. Of which AXA is manager and market maker... They invest in environment stocks, employing a complex stop-loss strategy.

Axa´s Stop-Loss strategy  ??? Method 1 “safe” If V 0 is fund size at day 0, invest the PV(V 0 ) in bonds, the remainder in (environment) stocks. After three months, invest PV(V 1 ) in bonds, the rest in stocks, etc. Method 2 “Risky” Invest all monies in stocks. Switch to all bonds as soon as value falls below PV(V t ).. - From the prospectus it is not clear whether they choose 1) or 2)… + Funds are “ringfenced”: no transfer to AXA other than management costs (max. 2.2% according to prospectus). Discussion question: what if everybody follows stop-loss strategies…

Leverage Products First there were warrants (covered warrants, option-scheinen), essentially bank-issued European style options on stocks, indices, baskets, etc. Very popular since the mid 90s. Mostly because they offer, due to issuer market making, lower bid-ask spreads than exchange initiated (American-style) option contracts. Traded mostly by speculating “hobbyists”. Around the turn of the millenium, two new types of products: 1) barrier options (down and out calls, up and out puts) 2) endless leverage certificates appeared

Barrier Options The first generation had a B > X (for calls). They could be interpreted as levered positions : If stock goes to €25.50 (+2%) Loan , Stock, Face value  Turbo goes to €5.50 (+10%, if you paid €5 ) Trading X = €20 at €25 Turbo If stock goes to €24.50 (-2%)  Turbo goes to €4.50 (-10% ) The first such instruments were called Turbos . They had a knockout level slightly above X , say B = €21 . If the stock drops to this level, the issuer would redeem the instrument, and return €1 . Since 2004 (or so) most banks issue barrier options with B = X . (and without residual value..)

Barrier Options (B=X) Payoff , Value S -PV( X ) Max (0 ,S-X ) If the underlying is traded in ‘continuous time’ Merton (1973) S X=B

Barrier Options (B=X) However, in reality, trade is not continuous… Payoff , Value Max(0, S -PV( X )) Max(0, S - X ) With jumps, days and nights. S

Barrier Options (B=X) The Gap Risk depends on the time of day Payoff , Value Max(0, S -PV( X )) Max(0, S - X ) At 9:05 S X=B

Barrier Options (B=X) The Gap Risk depends on the time of day Payoff , Value Max(0, S -PV( X )) Max(0, S - X ) At 17:25 S X=B

Barrier Options (B=X) How do we find the true value? Impossible to find a closed form solution… So, we use a Monte Carlo Simulation ,