Prof. Jayanth R. Varma's Financial Markets Blog

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Prof. Jayanth R. Varma's Financial Markets Blog, A Blog on Financial Markets and Their Regulation

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Wed, 31 Aug 2011

Can too much capital be risky?

An IMF working paper by Perotti, Ratnovski and Vlahu (PRV) published earlier this month argues that higher bank capital may not only fail to reduce risk taking, but may have an unintended effect of enabling banks to take more tail risk without the fear of breaching the minimal capital ratio in non-tail risky project realizations. PRV argue that the traditional minimum capital requirement must be supplemented with a maximum capital requirement (realistically, in the form of special attention devoted to banks with particularly high capital) in order to assure that they are not taking tail risk.

The key driver of this result is that, in the PRV model, banks choose between a relatively safe investment and a risky project which has both tail risk and non tail risk. Even though tail risk can be passed on to the government through explicit and implicit bail out, the non tail risk is borne by the bank. Banks facing high levels of non tail risk would rationally hold higher capital to protect themselves from the corrective actions imposed by the regulators when minimum capital levels are breached. In the PRV model, this high level of capital tells the regulator that the bank is bearing a large amount of tail risk as well.

In reality, banks can choose not only between safe assets and risky assets, but also between tail risk and non tail risk. For example, a bank which lends against a residential mortgage bears a significant amount of non tail risk and experiences volatility in earnings requiring capital even in normal situations. As against that, consider a bank that provides liquidity support to a special investment vehicle (SIV) that borrows short term and invests in senior and super senior tranches of a mortgage securitization. In normal times, the SIV earns a nice carry with virtually no risk because the senior tranches are unlikely to default except in systemic crisis events. However, the SIV faces catastrophic tail risk because of the high leverage. The liquidity support provided by the bank to the SIV transfers this tail risk to the bank. In normal times, the SIV produces no losses at all, and the bank produces smooth and predictable earnings with negligible losses. In times of systemic distress, the bank would take large losses, but the bank would rely on a tax payer bail out for coping with this tail risk. A rational bank would therefore set aside negligible capital for its SIV exposure because its non tail risk is low.

By setting up a model in which tail risk and non tail risk are embedded in the same project, the PRV paper does not capture the true risk profile of too big to fail (TBTF) banks that manufacture tail risk to monetize their TBTF status.

Posted at 17:21 on Wed, 31 Aug 2011     View/Post Comments (1)     permanent link

Mon, 29 Aug 2011

Safe assets as Giffen goods

Updated: corrected reference to absolute risk aversion instead of relative risk aversion and added a reference for the usage of the term return free risk.

The increased demand for US Treasuries after their credit rating was downgraded led some analysts to ask whether these assets are Giffen goods. The classic example of Giffen goods are staple foods like bread or potatoes where a rise in price depletes the spending power of the poor so much that they are no longer able to afford meat or other expensive food and are forced to consume more of the cheaper food. This means that the demand rises as the price rises – the income effect increases the demand of the inferior good so much that it outweighs the substitution effect of the higher price.

Can this happen with investment assets? For an investor trying to protect her capital, a rise in risk (without any change in the rate of return) of the safest asset is effectively an increase in the price of capital preservation. The idea is that a rise in risk of the safe asset consumes so much of the risk budget of the investor that she can no longer afford too much of the riskier asset. She therefore is forced to shift more of her portfolio into the safer asset. At a qualitative level, the story sounds plausible.

For a more rigorous analysis consider a portfolio choice model with two uncorrelated assets which we shall call the safer asset and the riskier asset. The following results can then be proved:

  1. In a pure mean-variance optimization framework, the safer asset can never be a Giffen good. An investor who had a positive allocation to the safer asset will reduce his allocation if its risk rises.
  2. In a more general expected utility setting, the safer asset can be a Giffen good. An investor who had a positive allocation to the safer asset could under certain conditions allocate even more to that asset when its risk rises.

I have written up a complete mathematical demonstration of the mean variance result for those who are interested. The intuitive reason for this result is actually quite simple. In a mean variance framework, the optimal portfolio consists of two components (a) the minimum variance portfolio which minimizes risk without any regard for return, and (b) a zero investment purely speculative portfolio of long positions in high return assets financed by short positions in low return assets. The allocation to the speculative portfolio is proportional to the risk tolerance (reciprocal of the Arrow Pratt measure of relative risk aversion) of the investor. An investor with zero risk tolerance holds only the minimum variance portfolio. As the risk tolerance increases, the investor blends the minimum variance portfolio with more and more of the speculative portfolio.

Now if the risk of the safer asset rises, its weight in the minimum variance portfolio necessarily declines. The weights of the two uncorrelated assets in the minimum variance portfolio are proportional to the reciprocals of the variances of the two assets and so a rise in variances reduces the weight.

So an investor with zero risk tolerance will necessarily reduce his holding of the safer asset when its risk increases. What about other investors? What will happen to the short positions that they hold in the safer assets through the speculative portfolio? Increasing the risk of the safer asset makes this short position riskier and all risk averse investors will therefore reduce this position by buying the safer asset. The question is whether this can outweigh the sale of the safer asset via the minimum variance portfolio?

Clearly this can happen if and only if the risk tolerance is very high. We can show that at such high levels of risk tolerance, the initial total position in the asset would have been short. Such an investor is not increasing his long position; he is only reducing his short position. This is not a Giffen good situation at all. Moreover, with short sale restrictions, the initial position in the safer asset would have been zero and it would just remain zero.

So in a mean variance framework, the safe asset is never a Giffen good. As one thinks about it, this result is being driven by the fact that in this framework, the risk aversion is being held constant in the form of a fixed tradeoff between risk and return. This does not allow the income effect to play itself out fully. The principal mechanism for a Giffen phenomenon is likely to be a rapid rise in risk aversion as wealth declines.

So I shift to an explicit expected utility framework using a logarithmic utility function with a fixed subsistence level: U(x) = log(x – s). This functional form is characterized by rapidly increasing risk aversion as the subsistence level s is approached. I consider an up state and a down state for the terminal value of the safe asset u1 and d1 with probabilities p1 and q1=1 – p1 respectively. Independently of this, the riskier asset also has two states u2 and d2 with probabilities p2 and q2=1 – p2 respectively. The investor invests w1 in the safer asset and w2 = 1 – w1 in the riskier asset. Expected utility is therefore given by:

p1 p2 log(w1 u1+ w2 u2 – s) +p1 q2 log(w1 u1+ w2 d2 – s) +q1 p2 log(w1 d1 +w2 u1 – s) +q1 q2 log(w1 d1+ w2 d2 – s)

The optimal asset allocation is determined by maximizing this expression with respect to w1. I did this numerically using this R script for specific numerical values of the various parameters. Specifically, I set:

s = 0.8, u1 = 1.01, d1 = 0.99, u2 = 5.00, d2 = 0.70, p1 = p2 = 0.50.

In keeping with the spirit of the times, the expected return on the safer asset is zero – instead of a risk free return, it represents return free risk. For these parameters, the weight in the safer asset is 81%. If we now reduce d1 to 0.90 (increasing the risk and reducing the return of the safer asset), the weight in the safer asset rises to 82%. Alternatively, if we change d1 to 0.85 and u1 to 1.15 (increasing the risk and leaving the return unchanged), the weight in the safer asset rises to 85%. The absolute risk aversion in the low wealth scenario rises from 7.4 when d1 = 0.99 to 15.7 when d1 = 0.90 and even further to 37.3 when d1 = 0.85. This is what drives the higher allocation to the safe asset. The safer asset is truly a Giffen good.

Posted at 03:31 on Mon, 29 Aug 2011     View/Post Comments (1)     permanent link

Mon, 22 Aug 2011

More on Law, Madoff, Fairness and Interest Rates

Last year, I blogged about a US bankruptcy court ruling which said that the net claim that a Madoff investor could make in court was for the total of all amounts invested less all amounts withdrawn. Somebody who invested $10 million in 1988 and withdrew $10 million in 2007 would be deemed to have got back his investment and would have no claims in the bankruptcy court. This ruling completely ignores the time value of money.

Grant Christensen, has written a detailed paper explaining the legal position regarding allocating losses in securities frauds, particularly Ponzi schemes like Madoff. Apparently, the bankruptcy courts “have a great deal of leeway when it comes to ratifying different methods to determine loss and allocate assets.” While the net investment method used by the court in the Madoff case is the most popular method, it is not the only method that is legally sustainable. The rescission and restitution method subtracts only the withdrawal of principal and does not subtract any interest or dividend that was withdrawn. Apparently, “appellate courts have expressed a clear preference for the rescission and restitution method over the net investment approach.”

Quite frankly, I have not been able to understand the mechanics of the various methods discussed in the Christensen paper. The economic difference, if any, between the rescission and restitution method (from civil law) and the loss to the losing victim method (based on criminal law) is not explained at all. The paper focuses on the legal foundations for various methods. I do know that some of the readers of my blog are lawyers and if they can throw light on this in the comments, that would be most helpful.

From what I have been able to understand, the alternative methods are based on accounting definitions of interest and principal. These would then be based on the promised rate of return which would be unrealistically high. Finance theory would suggest that the rate of return on a risk free asset (or a low risk asset) might be more appropriate. Alternatively, the average return earned by the Ponzi operator on the actual invested assets could be considered. For a successful Ponzi scheme, the cash inflows from new investors would exceed the cash outflows to withdrawing investors. This surplus cash would hopefully earn some return and this realized rate of return could be used as the discount rate.

Posted at 10:21 on Mon, 22 Aug 2011     View/Post Comments (0)     permanent link

Sun, 07 Aug 2011

HKEx Clearing House Risk Management Reforms

Last month, the Hong Kong Exchanges and Clearing Limited (HKEx) released a 73 page consultation paper on risk management reforms at the clearing house. Now, HKEx is nobody’s idea of best practices in risk management – this was after all the clearing house that needed a government bail out after the crash of 1987. Even today, the cash equities market of HKEx collects only mark to market margins and not initial margins – only the futures market collects initial margins. But, the HKEx consultation paper goes far beyond what most other exchanges have done and provides much needed transparency on the issue of clearing corporation risk management.

I have long argued that the international standards (the CPSS-IOSCO Recommendations for Central Counterparties, 2004) issued jointly by the BIS Committee on Payment Settlement Systems (CPSS) and the Technical Committee of the International Organization of Securities Commissions (IOSCO) are woefully inadequate. They only allow even the worst run clearing houses to claim to be compliant with global standards. Even the consultative report issued by CPSS-IOSCO earlier this year still falls well short of what is needed for such a systemically important entity as a clearing house.

What HKEx has done is to (a) explain (and strengthen) its stress testing procedures, (b) publicly admit that its guarantee fund is inadequate and (c) set out the process by which this guarantee fund will be built up to acceptable levels.

HKEx also states clearly that while some exchanges treat “margins” as a pooled resource, HKEx does not want to go down that path. It wants only the contributions to the guarantee fund to operate as a pooled resource. In other words, in case of a default, the exchange will have access to the margins of the defaulting member and the guarantee fund contributions of both defaulting and non defaulting members, but not the margins of the non defaulting members. Some exchanges are permitted under their bylaws to use even the margins of the non defaulting members. I believe that the HKEx is right in taking this “non-pooled upfront margin + pooled default fund” approach. In practice, if an exchange taps the margins of the non defaulting members, the market place would regard it as a default by the clearing house regardless of what the bylaws might say.

In conformity with Hong Kong’s well known plutocratic traditions, HKEx proposes:

To ensure long term sustainability and scalability of funding to support these changes and to mitigate any higher funding requirements for CPs that may detract from the markets’ competitiveness, we are keen to work with the HKSAR Government and the regulator in establishing a RMF which is funded by the SFC, HKEx and the market in equal proportion. The model is based on the principle that all key stakeholders, including the market players, the CCP and the regulator will support the stability of the securities and derivatives markets.

While reformers are struggling to avoid having to bail out the finance industry when things go badly wrong, HKEx is seeking a bailout in advance. We can see very clearly the moral hazard created by the 1987 bail out of HKEx.

Posted at 18:19 on Sun, 07 Aug 2011     View/Post Comments (1)     permanent link