Portfolio insurance

Q: How is portfolio insurance done?

A: One way to insure return on a portfolio is to buy a put option on the portfolio which will protect it against market decline while preserving the potential for gains when market rises. Another method is to create option position synthetically.

Q: What are the benefits of hedging a portfolio synthetically?

A: First, options market do not possess enough liquidity to absorb the trades fund managers carry out. Second, fund managers require options with strike price and maturity that are different from those traded on ET markets.

Q: How a synthetic option created?

A: To insure a portfolio synthetically, funds are divided between stock portfolio to be insured and risk less assets. When the value of the portfolio increases, the risk less assets are sold to buy stocks for the portfolio. But when the value of the portfolio decreases, then stocks are sold to buy risk less assets. The cost of insurance arises from the fact that the fund manager is always buying stocks when market rises and selling stocks when market declines.

Greek Letters

Q: What are Greek letters?

A: These are hedge parameters such as Delta, Gamma, Vega and Theta. Each represents a risk associated with the change in the market variable. When a FI writes an option in an OTC market it has to hedge its position in an OTC market itself. Where hedging is far more difficult than an ET market because the products are customised instead standardised. Each Greek letter measure a different dimension of risk in an option position. Aim of the trader is to manage all the Greeks in a manner that the risks become acceptable.

Q: What is Delta Hedging?

A: It's a hedging scheme designed with the purpose of making the price of the portfolio of derivatives insensitive to the changes in the price of the underlying asset i.e making the portfolio delta neutral. Since, delta of an option is always less than 1, number of shares needed to hedge an option position is always less than the number of shares on which the FI writes an option. Since the delta of an option is not constant and it keeps changing, the portfolio needs rebalancing i.e the number of shares required for hedging also keeps changing. There are two types of hedging schemes: Dynamic and Static.

Numerical Procedures

Q: What are the methods available to value derivatives contracts?

A: When the Black-Scholes formula is not applicable i.e the option payoff is path dependent and the option can be exercised prior to maturity as in the case of American options, there are three methods available. First, Binomial tree approach where the movement of the asset price is mapped on a tree. Second, Monte Carlo simulation where simulated value of future asset price is used to value derivatives. Third, Finite Difference Method where the differential equation is converted to a set of difference equations and then solved iteratively.

Q: What are the conditions under which these methods are applied?

A: MCS works from the beginning to the end of the life of the derivative. While both tree and FDM work in reverse. But MCS becomes less time consuming and more efficient when the number of underlying variable increases. But all three methods can be applied to both American and European options.

VaR: Value at Risk

Q: How VaR different from credit risk?

A: While the credit risk is associated with the probability of default by a counterparty in a derivatives contract. The VaR is about changes in the market variables to which any FI is exposed. It's a single number summarising the total risk to a portfolio of financial assets. Moreover, Central bankers also use this number to arrive at the capital required by the bank to reflect the risk its bearing. Specifically, VaR calculation is aimed at making a statement of the form: "We are X % certain that we are not going to lose more than $ V in the next N days."

Q: How is VaR calculated?

A: There are two ways of calculating VaR: The Historical Simulation approach and model building approach. The first approach uses past data to arrive at The joint probability distribution of market variables. But it is computationally slow and doesn't incorporate volatility updating schemes. The second approach is faster and can be used in conjunction with volatility updating schemes. But it assumes that market variables follow multivariate normal distribution, which may not be the case in practice.

EWMA, GARCH ...

Q: What EWMA and GARCH stand for?

A: EWMA is Exponentially Weighted Moving Average. While GARCH is Generalised Autoregressive Conditional Heteroscedasticity. These are models for estimating current and future levels of volatilities and correlations of assets for calculating VaR of a portfolio and valuing derivatives respectively.

Q: Among EWMA and GARCH, which is a better model for estimating volatilities and correlations?

A: Both model estimate present volatility using value of previous day's volatility and previous day's % change in market variable. Moreover, the weights assigned to observations decrease exponentially as observations become older. But in GARCH model additional weight is given to long run average variance rate, LRAV. Thus, theoretically GARCH is more appealing than EWMA model. The weights (model parameters) are estimated using MLM. Finally, a model is judged by how well it removes autocorrelation from the historical data using Ljung Box Statistics.

RWP vs RNP

Q: Why are the default intensities implied from historical data (RWP) much less than those implied from bond prices/equity prices (RNP)?

A: First, the corporate bonds are illiquid securities and bond traders demands extra returns to compensate for it. Second, bonds returns are highly skewed with limited upside. Thus, it's difficult to diversify risks in a bond portfolio than an equity portfolio. In practice, a bond portfolio is rarely fully diversified. Thus, a bond trader requires extra return for bearing this unsystematic risk in addition to the systematic risk. Third, bonds rarely default independent of each other, bonds defaults are correlated. The default rates vary from year to year depending upon economic conditions or that default by one company has a ripple effect resulting in default by other companies (credit contagion). This represents systematic risk and traders demand return for bearing this risk. 

Q: When one should use RWP and when RNP?

A: When valuing credit derivatives or  estimating the impact of default risk on the pricing of contracts one should use RNP. But for calculating expected future losses from possible defaults one should use RWP.

Market risk, Credit risk and default probabilities

Q: What is the difference between market risk and credit risk?

A: Market risk is a systematic risk to which any FI exposed. While the credit risk is a probability of default by borrowers or counterparties in a derivatives transaction.

Q: What are the methods for calculating these risks?

A: Market risk is calculated using VaR and Greek letters like Gamma, Vega and Theta etc. While the default probabilities for credit risk are calculated using historical data or Bond prices/Equity prices. The default probabilities calculated from historical data are real-world probabilities. While those calculated from bond prices/equity prices are called risk-neutral probabilities.

Q: Are these two probabilities different and if yes then why?

A: Yes, they are different because of the presence of expected excess returns over the risk free rate. If there were no expected excess return then the two probabilities would be same.

OTC versus Exchange traded products

Q: How the OTC market precipitated the whole financial crises?

A: OTC market is generally non-transparent, highly leveraged and provides higher profit margins to financial intermediaries than exchange traded products. And in some cases the contracts are not marked to market and no collateral is posted with the custodian. Commonly traded contracts on OTC market are currency and interest rate swaps and CDS. Thus, OTC traders are exposed to each other's credit risk. But the nominal value of outstanding OTC derivatives contracts at the end of 2008 stood at $592 tn, 10 times more than nominal value of $57.6 tn for ET contracts. When housing market sank and with it the mortgage backed securities, AIG took a hit as the seller of CDS written on MBS. And a CDS is an OTC contract.

Q: What is a Credit Default Swap?

A: A CDS is a derivative contract bought by lenders as an insurance against a possible default of credit by the borrowers. The FI writing the CDS agrees to buy the bonds at their face value ( principal amount) in the case the borrower defaults on its payment. The total face value of the bonds of which CDS is written is known as notional principal of that CDS. During late 90s and early 2000s, banks made extensive use of CDS to transfer credit risk to other parts of financial system.

Low quality debt into high quality

Q: What went wrong with the process of securitisation?

A: This financial crises had roots in the way Mortgage market evolved. In the 1970s Federal Home loan mortgage corporation was established. It securitised the home loans by creating Mortgage Backed Securities and allowed US government to transfer market risk to investors. But a Wall Street investor cannot invest in sub-investment grade instrument. An MBS was a sub-investment grade security. To improve the quality of an MBS, they were pooled with other high quality debt instruments in the form of Collateralised Debt Obligation, CDO.

Q: What went wrong with CDOs?

A: CDO is a way of creating securities with different risk characteristics from a portfolio of debt instruments. These different securities are called tranches. The tranch which takes on the initial losses offers the highest return or yield. While the tranch which incurs residual losses receives the lowest return. In the year preceding the crises, outstanding CDO volume stood at $ 900 bn. Of which 17% was created from sub-prime mortgages. 

Arrogance

Q: If eventually the Banking system had to be "bailed out" then why Bear Sterns and Lehman Brothers were allowed to go bankrupt in the first place?

A: It was a sort of moral posturing by the Fed that eventually failed. The Fed was perceiving it as a creative destruction process which was expected to remove the imbalances in the system. After all it is the absence of state intervention in the markets that makes America different from other developed or large economies like Japan and China. But the gambit failed because the next day when Merrill Lynch was staring at the same fate, BoA had to buy it.

Q: But aren't the treasury guilty of another crime. That of running a low interest rate economy which led to excess liquidity and consequent high inflation and finally stock market bubble?

A: Yes, the Bush administration ran unprecedented fiscal and current account deficits to finance- wars, tax cuts and public over consumption, all fuelled by debt. And until 2007 i.e before the crash, all of this excess liquidity was absorbed by asset price ( about $8 tn) and commodity price inflation ( especially oil prices, $3 tn). But why blame the treasury. It is only the supplier of credit. Aren't the borrowers ( like banks, industry and consumers) equally culpable of succumbing to the temptation.

Quantum of Loss

Q: The losses were huge in number, running into billions and trillions of dollars. So huge that they can expressed as a percentage of US GDP?

A: To keep the numbers in perspective. First, The US GDP stood at $17 trillions in 2015. Second, during and after the crises $600 bn of net worth was written down by the financial firms. Finally, the budget for Troubled Assets Recovery Program (TARP) proposed by Fed and U.S. treasury stood at $700 bn.

Q: The net worth of executives running these banks also ran into billions of dollars. How much hit they took when the market crashed?
A: A major chunk of the compensation given to the bankers was in the form of stock options. When the markets crashed, with them the the value of stock options also took the plunge. Overall, major bankers saw their valuations falling about 60-100% of their net worth. Jimmy Cayne's (Bear Sterns) worth was reduced to $61 mn from $1.6 bn. Similarly, Richard Fuld's (Lehman Brothers) billion dollar valuation was not even worth half a million dollars after the crash.

Q: Should we be sympathetic to these bankers for like the retail investors they too felt the pain of the crash?
A: How can you expect the "retail investor" to be sympathetic to someone with a net worth of millions even after the crash. Moreover, the havoc they unleashed over the financial universe was of their own making.

Q: The fact that they received compensation in the form of stock option speaks of the belief they had in the financial system?
A: It is difficult to say whether it was their "belief" or was it simply their "arrogance" in the financial architecture they created and ran.

Crossing the line

Q: How a derivatives transaction be speculative in nature?

A: In any transaction involving two counterparties, if one party is reducing its risk then the other side is assuming it. For example, in case of options, the side buying the option by paying "option premium" is reducing its risk. While side receiving "option premium" is assuming the risk, i.e "writing option". Now writing an option is no doubt an speculative activity. 

Q: Is there any other speculative activity which resulted in huge losses for these banks?

A: Yes. Currency swaps i.e. swapping one currency exposure with a low interest currency was another major loss making derivatives transaction. Other activity was taking on "Leverage" i.e. making investments based on borrowed capital.

Q: But what forced or encouraged these banks to participate in speculation?

A: Traditionally banks relied on passive depositors - mainly working, middle class people, who keep their savings accounts, as a source of funds- for their financing requirements. But now these same passive depositors are becoming active investors in the stock market. In essence, banks are now dependent on "volatile" investors that the securities markets depends upon.

Role of regulators

Q: The banks which went bankrupt were not operating in isolation. If they were meddling in instruments as complex as derivatives then why the banking regulators didn't intervene when they could have made a difference?

A: First, these were no ordinary banks. Lehmann Brothers e.g is more than 150 years old. Nobody expected them to fail. Second, if it were ordinary lending-borrowing type banking. Then there are strict Basel regulations to govern them. So, even though use of derivatives has recently become widespread. They are still in nascent stage and hence not strictly regulated.

Q: But how can a bank incur such huge losses by trading in derivatives? Isn't it a known fact that derivatives have limited downside for loss while retaining unlimited upside potential for profits. 

A: Derivatives are used for the purpose of reducing your risk, i.e. a bank's exposure to market uncertainties, also known as hedging. But since there is also a possibility that one can reap profits by entering into such a derivatives contract, the counterparties cross the line from hedging to speculation. An activity a good banker should strictly avoid.