the use of structured products applications, benefits and limitations for the institutional investor

For a retail institutional investor, structured products present new ways to reach the investment needs of clients by adding new products to the product basket, preserving the level of d

The use of structured products:

applications, benefits and limitations for the institutional investor

Submitted by Anna Georgieva

Supervisors: Marcel Koebeli, Marc Chesney, Pascal Botteron

December 2005

3 The institutional investor

3.1 Business needs and risk preferences

3.2 Institutional investors: readily invested in a structured product on the economy

3.3 Structured products, Indexation and the Core-satellite framework

4 Limitations of structured products as investment vehicles

0 Introduction

The institutional investor is in the business of understanding, pricing and managing risks to earn a return for the benefit of all stakeholders In this paper I discuss how structured products can be used by institutional investors

In a perfect world (Arrow-Debreu state-claim framework) there exist enough securities to recreate any payoff Some assumptions of this idealized world are: there exist basic securities, Arrow securities, that they have a risk-free payoff in any state, no transaction cost, no information asymmetry, all

investors have the same expectations Then derivatives are redundant instruments, as they can be replicated The price of the replicating strategy should be equal to the price of the derivative; otherwise there is an arbitrage opportunity

Several research papers discuss the optimal existence of derivatives [Merton 1971], [Carr Madan 2001], [Carr Madan 1998], [Liu Pan 2003], [Ross 1976]) The research results are usually dependant

on assumptions about the process of the underlying The case of including derivatives in an investor’s portfolio is usually solved making the assumption that investor preferences follow a certain

mathematical function The optimal investment in derivatives is then determined as the solution which maximizes the investor’s utility function A closed form solution may or may not be available

depending on the assumptions about the underlying process and the utility function

I treat the problem in a practical, applied way Needless to say, financial markets have readily justified the existence of derivatives and derivatives related products The focus is on how structured products can be handy to an institutional investor, as opposed to how do we price, replicate and hedge them While in the back of every properly priced derivative there is a lot of mathematics, in this paper I focus on the investment interpretation and application

I present structured products as a natural investment choice of an institutional investor who faces the business constraints of a liability stream and of stakeholder and client expectations Their main

applications are in creating risk-return flexibility, isolating risks and providing exposure opportunities

I point at possible specific applications, but there is no almighty product that will magically solve all investment problems and unless a specific investor is consider it is impossible to make a strong

statement about the best choice

For a retail institutional investor, structured products present new ways to reach the investment needs

of clients by adding new products to the product basket, preserving the level of distribution fees and increasing the ability to raise new money

For the pension or trust fund investor, in particular in a core-satellite framework, structured products provide payoff flexibility, bundled or unbundled exposure to new and old asset classes, and can be optimally added as satellites to the investment portfolio

For the asset manager in an insurance company, structured products stand out with their ability to implement sophisticated investment views, and to isolate and hedge risks

Research on the pricing and replication of some of these structures are widely available; others do not have a closed-form solution The most flexible approach is using Monte Carlo (MC) pricing tool Based on the martingale approach of derivatives pricing, this approach can price any possibly payoff and has gained widespread acceptance among practitioners

1 What are structured products?

1.1 A definition

Structured products are investment instruments that combine at least one derivative with traditional assets such as equity and fixed-income securities The value of the derivative may depend on one or several underlying assets Furthermore, unlike a portfolio with the same constituents the structured product is usually wrapped in a legally compliant, ready-to-invest format and in this sense it is a packaged portfolio

The usual components of a structured product are a zero-coupon bond component and an option component The payout from the option can be in the form of a fixed or variable coupon, or can be paid out during the lifetime of the product or at maturity The zero-coupon bond component serves as buffer for yield-enhancement strategies which profit from actively accepting risk Therefore the

investor cannot suffer a loss higher than the note, but may lose significant part of it The zero-coupon bond component is a floor for the capital protected products Other products, in particular various dynamic investment strategies, adjust the proportion of the zero-coupon bond over time depending on

a predetermined rule

From an economic point of view, the structured product can be broken down in two main components:

Investment view + Payoff structure = Structured product

The investment view is driven by factors such as:

• Investor expectations towards the underlying: bearish, flat, bullish, range bound, ladder etc

• Choice of underlying The underlying may be available in a readily investable format or has to

be synthetically extracted:

o Single stock

o Basket of stocks

o Index or multiple indices

o Mutual fund, hedge fund, Fund of Hedge Funds, discretionary manager

o Systematically rebalanced strategy

o Volatility, correlation, dispersion

• Cash flows timing: periodic coupons from an underlying that pays none; total lump payment when underlying pays coupon; variable coupon or fixed coupon; fixed coupons during certain periods of the life of the product etc

• Risk profile: leverage, conditional capital protection, partial capital protection, full capital protection

• Maturity: Short-term, medium-term or long-term

The importance of both components is evident when we look at the fundamental exposure types in the next section The focus here is that despite the fact that the option types have been known for a long time, the investment view gives them a different interpretation

1.2 The fundamental exposure types

The fundamental exposure types are the generic option payoffs Combining these with a long zero coupon bond gives the primal structured products, some of which have not failed to go out of fashion Figure 1 shows clearly the interaction between investment view and payoff structure Some authors seem to refer to prefer bullish payoffs, and consider only the payoffs in upper row of the table,

corresponding to the bullish investment view as structured products

Fundamental exposure types

Delta one

(Certificate)

Capital protected products -

Yield enhancement products

The Delta one (certificate) provides full exposure to the underlying Investor gains wealth as underlying appreciates and loses wealth as the underlying depreciates The payoff is the same independent of the investment view The other 4 payoffs are:

1) Bullish investment view, yield-enhanced or return-enhanced exposure – capped upside,

unlimited downside Investor prefers to sell the upside potential and receive a higher return Investor is actually bullish on the underlying, but prefers to cash in the expected return, rather than wait for the uncertain appreciation to realize Investor practically accepts the downside risk of the underlying and receives a premium for that, which results in a higher yield

compared to the underlying

2) Bullish investment view, capital protected exposure – floored downside, unlimited upside The investor pays a premium to ensure downside protection, but keep the upside exposure

3) Bearish investment view, yield-enhanced exposure – capped upside, unlimited downside However the structure pays of when the underlying decreases in value

4) Bearish investment view, capital protected exposure – floored downside, unlimited upside Again the structure pays as expected if the underlying decreases in value

Typically, only payoff type 2), the long call, payoff is considered a capital protected payoff Yet for an outright bearish investor, this payoff is detrimental as it leaves him exposed to an appreciation of the underlying

The investment view is intrinsically connected to the split between yield-enhancement products, where the investor chooses the higher risk-return combination, and capital protection, where the investor prefers a lower risk-return combination

These generic payoffs have been embraced by the market I show 3 widely known products that can be directly matched to 3 of the generic payoffs and also present an investment case for their use These are:

1) The Delta One (Certificate) (Figure 2 & Figure 3)

2) The Reverse Convertible – as an example of bullish yield-enhancement payoffs (Figure 5

&Figure 4)

3) The Capital Protected Note – as an example of bullish capital protected payoffs (Figure 6)

Other payoff structures cannot be easily classified as only yield-enhancement or capital protected type

I discuss some of them Section 2.1

‹ The investor receives the full upside and downside of the underlying.

‹Certificates are a flexible way to invest in customized baskets and implement fundamental long-only investment ideas.

‹ Investor goes long a zero strike call.

‹ Short-, mid- to long-term investment horizon.

‹ Investor wants full exposure to the underlying.

Structure

Payout

Investment idea

Delta One (Certificate)

Certificates have the same payoff as the underlying

Underlying price Performance

100 Initial price Time

Price

100

‹ Our investment view is based on an expected increase in peak sales of new products,

industry cost savings as the sales mix shifts towards secondary care, and positive volume

outlook in the US as new prescription drug benefits for seniors start in the end of 2005.

‹ Structure

– We go long a zero strike call on a basket of the following stocks: AstraZeneca, Novartis,

GlaxoSmithKline, Essilor International, Merck, Pfizer, Cardinal Health Inc.

– The basket can be equally-weighted, performance-weighted or custom-weighted.

– 3 year maturity.

‹ The certificate pays the performance of the basket.

‹ Very low structuring fees.

Certificate on a Pharmaceutical Basket

We are bullish on European pharmaceutical companies

Figure 3

Figure 2

Reverse Convertibles

Reverse Convertibles are yield-enhancement strategies with short maturity

‹ A coupon is always paid.

‹ Depending on the product features the investor is exposed to a different degree to the downside of the underlying.

‹ Investor go long a zero-coupon bond and short a put, or a short DIP put

‹ Short-term investment horizon

‹ Moderately bullish or range bound view

Structure

Payout

Investment idea

Time Price

100

100 Initial price

13

Performance

‹ Given the barrier for the DIN put or the strike for the short put we solve for the coupon.

‹ The lower the barrier level the lower is the coupon.

‹ This is a very popular yield-enhancement structure for a bullish investor.

Performance

Barrier

Underlying price

100 Initial price

Priced examples

8.47%

1 year 80%

Porsche

1 year

No barrier Porsche

Maturity Barrier Underlying

Reverse Convertibles on Porsche

3 examples with different barrier levels

Figure 5

14

Figure 4

Capital Protected Notes (CPN)

Capital protected notes are downside protected investments

‹ 100% of invested capital plus a coupon (or upside participation).

‹ We go long a zero-coupon bond and long an option with upside exposure.

‹ Short-, mid- or long-term investment horizon.

‹ Bullish on the underlying, but we want downside protection.

Structure

Payout

Investment idea

Underlying price Performance

100 Initial price

Lower capital protection with higher participation rate

Time Price

2 Applications of structured products in the portfolio of an institutional investor

In a general framework, the two applications of structured products are payoff flexibility and isolating

or bundling risks

1 Payoff diversity and flexibility, payoff timing flexibility, leverage

It is almost impossible to define payoff diversity and flexibility that structured products can provide I present six structures that exemplify the payoff flexibility and diversity that structure products can offer These are:

1) The Autocallable (Figure 7, Figure 8 &Figure 9)

2) The Reverse Convertible Autocallable (Figure 10 & Figure 11)

3) The Springboard (Figure 12)

4) The CertiPlus (Figure 13)

5) The Plain Turbo Certificate (Figure 14)

6) The Leveraged Airbag (Figure 14)

The Autocallable and the Reverse Convertible Autocallable can be easily classified as

yield-enhancement products The Springboard is a capital protected product However the Certiplus, the Plain Turbo Certificate and the Leveraged Airbag cannot be easily classified into one of the

fundamental exposure types, because they are vehicles to express sophisticated investment views

All examples are applied to a single stock underlying Considering how central correlation is in the pricing of baskets, I present examples in section 2.2

The autocallable acts as a rational investor who has a range bound view on the underlying If the

underlying appreciates enough, it is autocalled and the structure ceases to exist, that is, the payoff is as

if the investor has taken profit on the underlying On the other hand of the underlying stays underwater, the investor receives a coupon The worst-case scenario occurs when the underlying goes down by more than the investor expected Then the investor will receive the bad performing underlying, but this loss is nevertheless partially offset by the coupons that the investor receives until maturity

Autocallables

Autocallables are yield-enhancement strategies

‹ The structure autocalls if the underlying is above the trigger level in the years before maturity The investor receives a coupon equal to the number

of years multiplied by the initial coupon level.

‹ If underlying matures above the initial level and has not been autocalled, investor receives a coupon equal to the number of years multiplied by the initial coupon level.

‹ If underlying matures between barrier and initial price, investor receives 100% back.

‹ If the underlying matures below the barrier, investor receives only the performance of the underlying This is the worst-case scenario.

‹ We go long a zero-coupon bond, short a down-and-in put (DIP), long a series of binary calls

‹ High likelihood of coupon payment and partial protection.

‹ Short- to mid-term investment horizon.

‹ Range bound view on the underlying.

‹ The 4 scenarios show the representative payoffs of the autocallable structure.

‹ In case 1 the structure ceases to exist after period 1, in all other cases it matures after 3

Porsche

Invested amount Coupon

Maturity Barrier Underlying

Time Price

65

Autocallable of Porsche

Underlying price

100 Initial price

Coupon

Barrier level

Underlying price Performance

100 Initial price

Coupon

Barrier level

1) Autocalled at the end of period 1; Investor

receives 100% of invested capital + coupon.

2) Product continues until maturity and pays

100% of capital + coupon equal to =

(number of years * coupon).

3) Product continues until maturity; Investor

receives 100% of invested capital only.

4) Product continues until maturity; investor

receives the performance of the underlying.

Underlying price

100 Initial price

Barrier level

Time Price

Autocallable Reverse Convertible

10

tf

UNDERLYING UNDERLYING

‹ An autocall occurs in year i if the following occurs

‹ Example for Swiss underlyings, 3 years, 60% Barrier, CHF

UBS Novartis Roche Swiss Re Ciba Credit Suisse

Coupon

Barrier level

Underlying price Performance

100 Initial price

Coupon

Barrier level

1) Autocalled at the end of period 1; Investor

receives 100% of invested capital + coupon.

2) Product continues until maturity and pays a

coupon every year 100% of capital is

repaid at maturity.

3) Every year a coupon is paid At maturity the

investor receives 100% back

4) Every year a coupon is paid Since the

barrier is triggered the investor receives the

performance of the stock at maturity.

Underlying price

100 Initial price

Time Price

Autocallable Reverse Convertible

Autocallable on the Spread

Figure 10 & Figure 11

Underlying price Performance

100 Initial price

Springboard

The Springboard profits from a sophisticated upside exposure view

‹The springboard provides leveraged exposure up to the level of the short deleveraged call

‹Long leveraged zero-strike call, short deleveraged call

‹Short- to mid-term investment horizon

‹Bullish range bound view

Structure

Payout

Investment idea

Time Price

CertiPlus

The CertiPlus products combine downside protection up to a certain level and upside

potential

barrier level and the strike level, but we are exposed to the downside below the barrier

Structure

Payout

Investment idea

Time Price

100

Figure 13

‹Plain Turbo Certificate

– Outperformance between the 2 strikes.

– Full downside exposure.

– Long ATM call, long zero strike call,

short 2 OTM calls.

– Short-term investment horizon.

Variations

Turbos generate an Outperformance compared to the Underlying

Underlying price

100 Initial price Cap Level

‹ Leveraged Airbag

– Outperformance on the upside and partial

downside protection.

– Long zero strike call, long ATM put,

short a leveraged OTM put, long a fraction

of an ATM call.

– Mid-term investment horizon.

Underlying price

100 Initial price

Strike Level

Performance

Performance

Figure 14

2 Isolating risk and gaining exposure: volatility, correlation, inflation, credit, hedge funds

Structured products provide the capacity to isolate and trade asset classes that are mixed-in in

traditional assets or may not be directly investable due to constraints on the asset side or the investor side I look at 5 specific investment classes: volatility, correlation, inflation, credit and hedge funds

Not all of them are recognized as asset classes; however the existence of structured products shows

investor interest

An asset class is a set of investments that exhibit similar and distinctive investment characteristics

(return, volatility and relationship to the returns of other investment assets) The asset class represents

a distinctive type of risk For accepting this risk any rational investor expects to earn an appropriate

return The rational investor judiciously accepts risk and expects an appropriate return

2.1 Volatility

Derivatives are both directional and volatility instruments (Neftci provides an excellent exposition)

That is, the investor makes a bet both on the direction which the underlying will take and on implied

vs actual volatility If the actual volatility exceeds implied volatility the long side of the transaction

will realize a profit, assuming all other factors the same Vice versa, if the actual volatility is lower that implied volatility the short side of the transaction will realize a profit at the maturity of the option

Volatility is an exogenous input in the Black-Scholes (or another pricing formula or Monte carlo

simulation) and it shows the volatility view of the investor

The specific dynamics of volatility can be summarized in the following 4 points

• It jumps when the market crashes

• It reverts back towards its long-term mean

• It experience high and low regimes

• It is usually negatively correlated with the underlying asset return

[GM 1998], [Qu 2000] discuss volatility as an asset class [Carr and Madan 1998] provide the

replication and pricing formula for volatility and variance swaps

Volatility structured products can be used to make sophisticated bets on volatility An excellent

exposition on the pricing of volatility products are the classic [Derman ??], [Hosker ??] and [Mougeot 2005] The following table summarizes some of the applications

Delta-hedged option

Variance swap

Gamma swap

Conditional variance swap

Corridor variance swap

Correlation swap

While volatility swaps on currencies exist, the main application seems to be in equity index and swap rate volatility For an indexed investor, the volatility swap is of direct interest as it can help be used to manage the tracking error Apart from the swaps presented above, other volatility products are:

• Volatility options – An example is a call option on volatility The option gains rapidly in value when volatility increases sharply

• Volatility swaps combined with equity futures – volatility swaps entail an implicit directional view on market price movements There is evidence of negative correlation between the equity market performance and the level of volatility Volatility tends to be high during market

crashes Thus, the seller of volatility swaps has an implicit expectation that the equity market will increase in values and the buyer has an implicit expectation that the equity market will decrease in value To hedge the directional effect of the volatility swap the investor can trade equity futures

• Volatility bonds – the coupon is proportional to the difference in the swap rates of a certain maturity, for example the 20 year swap rate, between the start and the end date of each year The investor is buying a series of 20 year swaption straddles

Here I show an example where variance swaps can be directly used to hedge secondary guarantees offered by insurance companies Secondary guarantees exist in two forms: death benefits and living benefits Among living benefits the most popular product are the guaranteed minimum withdrawal benefits (GMWBs), which guarantee the principal, may allow step-ups and allows set percentages of withdrawal each year, even if account values is zero The key attraction to customer of this product is the protection against another bear market and they give life insurers a competitive advantage over mutual fund providers

The main risk for the insurer offering such a guarantee is a prolonged equity downturn which poses a

“catastrophe” type risk The GMWBs will go deep in the money potentially creating large losses for the insurance company if they are not properly hedged

Because secondary guarantees are long-term illiquid benefits with liabilities that are expected to extend over a 20-30 year time period and contain the uncertainty of policyholder utilisation rates, there are essentially no financial derivatives that can be found to form a perfect hedge Even if derivatives were available for 20-30 year periods, the counterparty risk over such long durations would be

unacceptably high

The long-term illiquid nature of the benefits means that they are suited to dynamic hedging strategies The insurer will establish a portfolio of fairly short-dated futures and put and call options which can be rolled over providing a rolling hedge to offset the guarantee risks based on assumptions about future market behaviour and policyholder utilisation The dynamic element of the strategy lies in using futures and options that are typically fairly short dated at around 3-9 months as these are normally the most liquid By rolling the positions over and adjusting those to reflect changes in the book, often on a daily basis, a fairly effective continuous hedge against most market risks can be achieved

The three Greeks of concern are:

Delta Change in the market value of the

fund

Equity Futures Vega Change in the market volatility Put and call options (straddles)

The straddles are the easiest way to partially hedge volatility, however they do not provide pure exposure to volatility The problem with the straddle is that once the stock price has moved away from the initial level, the straddle delta is not zero anymore Also, since both options are initially in the money, straddles are usually expensive

For the insurance company, the variance swap is the best hedging solution The variance swap is a forward contract that pays at maturity the difference between the realized variance of an underlying and the initially defined variance strike price K

‹ Carr and Madan show that the variance swap can be replicated by a continuum of puts and

calls inversely wghted by the sware of their strike price The solution is model-free

‹The perfect hedge involve buying a continuum of put with strike from 0 to Fo, the current

level, and buys a continuum of call options with strikes from Fo to infinity:

The Variance Swap

Buyer and seller exchange payments based on the level of variance

1)

(12

]

0 2 0,

0 2

F F

rT T

K dK

K P K T

While in linear payoffs correlation and volatility are positively correlated, there are payoffs where the investor can profit from high volatility and low correlation of the stocks in the basket These are the so-called dispersion payoffs I give an example to show why such a product can be interesting for an investor

Correlation is usually measured as

B A

B

A

B A

i

i A B B A

n B A Cov

1( )( )

1),

1

A i

A i i

S

S A

−

i

A n

A

1

1

This formula clearly makes the assumption that the log returns of the two assets are normally

distributed, and may underestimate or overestimate true correlation if this is not the case

Correlation is a measure of the diversification and is closely linked to the volatility of the basket

To show the link between correlation and volatility, let us consider a basket of two stocks, A and B, and assume that both have a constant volatility of 25% As the correlation increases from -100% to 100% the volatility of the basket will increase at a decreasing rate and will finally be equal to the arithmetic average of the volatilities of the two stocks (Figure 16) The non-linear rate of decrease is due to the fact that volatility is a power function in correlation

Correlation is also the measure of diversification Correlation is low when the stocks in the basket move apart, and is high when the stocks in the basket move concordantly When the market is bullish and correlation is high, the investor wants to be long correlation, so that he can profit from the

leverage effect Yet, when market is bearish and correlation is high the investors wants to be short correlation, so that he can benefit from the diversification effect

Dispersion bets are bets that stocks in the basket will move in different directions The best payoff is achieved when we take the difference between the best performing stock and the worst performing stock This can be achieved through a combination of a long lookback call plus a long lookback put

This is obviously the primal volatility trade, and due to the lookback feature it can be prohibitively expensive

With the proper payoff structure, the dispersion of the stocks in the basket can generate higher IRR or consistent and uncorrelated performance

First, I compare the price and the IRR of a structured product that pays off the average of call spreads

on a basket of stocks and a structured product that pays the call spread on the average of basket of stocks I introduce the floor and the cap in order to obtain financially sensible prices and results

Basket of Call Spreads

The coupon is the average of the call spreads on the underlyings

‹ 100% of invested at maturity.

‹ The coupon depends on the return of the stocks in the basket and is capped.

‹ The annual coupon is paid accordingly to the following formula:

‹ We go long a zero-coupon bond and 3 long call spreads on the indecis.

‹ Mid- to long-term investment horizon.

‹ Moderately bullish on a basket of 3 indices (NKY, SPX, FTSE)

‹ But we want downside protection.

3 1

i

CapLevel Index

Index FloorLevel

Max

Figure 17

Call Spread on a Basket

The coupon of the Call Spread on a Basket depends on the average performance of a

basket

‹ 100% of invested at maturity.

‹ The coupon depends on the average return of the stocks in the basket and is capped.

‹ The annual coupon is paid accordingly to the following formula:

‹ We go long a zero-coupon bond and a long call spread on the indices in the basket.

‹ Mid- to long-term investment horizon.

‹ Moderately bullish on a basket of 3 indices (NKY, SPX, FTSE)

‹ But we want downside protection.

1

t i,

, Index

Index Min

x 3

1 , CapLevel FloorLevel

Performance of the 3 indices during the backtest period 20-Dec-1990 until 20-Dec-2005

Figure 19

The correlation matrix fed into the MC prices is the same (3 year period 2002 until

Price and IRR Comparison

(top) and historical IRR

0.7% to 3 .5%

3.5% to 7 .7%

7.7% to 1 1.9%

11.9 % to 16.1 % 16.1 % to 20%

Call spread on basket Basket of call spreads

Call spread on basket

Basket of call spreads

Basket of call spreads