Excessive risk-taking and irrational behaviour have often been blamed for the failure of the financial markets during the crisis.
Financial products take a view on the properties of the underlying and try to optimise the payoff. While many models exist for this purpose, factoring into their design the model risk associated with the underlying assumptions is still quite tricky.
"The major drawback of the current methods in designing structured products is the disconnection between incentives of structurers on the one hand, versus other stakeholders in an organisation, such as creditors – or in the economy, for instance, tax payers - who may have a divergent appetite for risk," says Michael Jacobs, a principal director and lead of the modelling and validation practice in the finance and risk analytics division at Accenture in New York.
"The risks of model failure, and its costs, are not explicitly part of the modelling process or consideration for structurers, and risk management has to intervene as a reaction to this."
In this month's first technical, Elasticity theory of structuring, Andrei Soklakov, head of strategic development for Asia-Pacific equities at Deutsche Bank in Hong Kong, proposes a product structuring technique that is able to remove excessive risk-taking or gambling-type behaviour by controlling payoff design mathematically.
Investments can typically be viewed as an optimisation problem, where a utility function is optimised given constraints – for instance, maximising returns. If the utility function is concave, the investor is risk-averse and enjoys less utility as the returns increase. In this case, as the investor makes more and more money, the utility of an extra fixed amount of return decreases. The opposite of that is considered risk-taking behaviour. Risk appetite is easy to identify and model mathematically, but is not applied to product structuring.
Despite its key role in market behaviour, risk appetite is often a separate function in product structuring. Although investments are optimised for risk measures such as volatility, risk appetite can change in an irrational way
"There is an optimisation problem that legacy investment products aren't able to articulate. This optimisation problem has a structure depending on whether you are risk averse or you are gambling. Mathematically it's possible to know which is which," says Soklakov.
Soklakov's paper uses what is called a growth-optimising investor – who only seeks to maximise returns and does not care about risk – as a benchmark. The paper then adds a risk aversion profile to the growth-optimising investor, which shows where on the distribution of the returns an investor would want to have a certain risk appetite.
Modelling risk aversion mathematically allows a structurer to factor-in risk appetite in a logical way instead of basing it on intuition or a sudden appetite for much higher returns on a new investment with potentially large downside risk. This way, irrational behaviour can be controlled.
Soklakov does this using the market-based implied probability distribution of the underlying, and the investor's own view of the probability distribution. The payoff of a growth-optimal investor can be derived by dividing the latter by the former. He then adds a risk aversion profile to the growth-optimal payoff using Bayesian theory of information to derive his final result, called the payoff elasticity equation. The profile allows investors to choose what appetite they want to apply at different points of the distribution. If the risk aversion is 1, the payoff is the same as that of the growth-optimising investor.
"For instance, we can say ‘I'm OK with going with the growth-optimising investor in this small area near-the-money'. I'm sure about my view there, but then I want to increase risk aversion as I depart from the area I'm comfortable with," says Soklakov.
Some hedge funds are already known to be using the technique in structuring interest rate investments.
Risk aversion is an important aspect of investor behaviour. In 2014, Jon Gregory, a partner at Solum Financial, took a fresh look at the failure of the collateralised debt obligations (CDO) market during the crisis by arguing the CDOs didn't fall due to incorrect correlations, which at the time was touted as the main cause of the product's downfall, but because the risk aversion of investors increased.
One way this could have been prevented was if the rating agencies had penalised the credit ratings of the products in the run-up to the crisis. This would have increased the risk aversion on the products and caused people to invest less in them – so a steep increase in correlation would not have caused the market to fail.
Despite its key role in market behaviour, risk appetite is often a separate function in product structuring. Although investments are optimised for risk measures such as volatility, risk appetite can change in an irrational way. Perhaps, an important step in moving away from the mistakes of the crisis would be to tie-up risk appetite with product design in a logically consistent way. At the end of the day, appetite is what ultimately drives markets.
Click here to view our second technical paper for December: Beat equal weighting: a strategy for portfolio optimisation
The week on Risk.net, March 10-16 2018Receive this by email