Exploring the use of Kelly Criterion for Basel Capital Requirement: an Optimal and Countercyclical Approach
Journal of Risk Management in Financial Institutions, Vol. 8, 1 45–61
Author: Max Wong
The Basel capital is a “margin” requirement imposed by regulators to cushion banks against extreme falls in prices of assets held on its balance sheets, and is often a function of value-at-risk (VaR). The way banks adjust their balance sheets to maintain the requirement is equivalent to leverage targeting that has been shown to cause endogenous and procyclical risk. The 2008 crisis revealed that Basel II capital was insufficient to protect banks against crisis losses, but the industry believes the current Basel III requirements are too high for sustainable business. Is there an optimal capital?

Balance sheet rebalancing with a target leverage can be described by a multiplicative game or process. Most players will lose money even if the game has a positive edge because suboptimal or excessive leverage causes many players to get wiped out over time and the system achieves a “winner takes all” effect. Fortunately, the Kelly criterion provides an optimal leverage that could mitigate this curse of leverage. Treating a bank as a player in this multiplicative process and using balance sheet simulation, we show that the Basel’s capital approach is suboptimal and the Kelly criterion gives a capital requirement that provides the best survival strategy over the economic cycle. The article suggests how this can be computed in practice for an actual bank.

We found that a Kelly-based capital is potentially countercyclical, and could reinforce the central bank monetary policy transmission mechanism. Thus, it is useful for macroprudential regulation.

Full version available at SSRN: http://ssrn.com/abstract=2350041
Market BuVaR: A Countercyclical Risk Metric
  Journal of Risk Management in Financial Institutions, Vol 4(4), 419-432.
Author: Max Wong
The malfunction of the Value-at-risk (VaR) model is a risk management failure during the 2008 credit crisis. This metric is now criticized for being too little, too late. We propose an improvement - making VaR countercyclical and more robust to fat-tails. The new metric is called, bubble-VaR (BuVaR), the expected shortfall of a trading book portfolio removed of the effects of procyclicality. It involves inflating one side of the return distribution of an asset by a scaling factor called bubble that depends on the location of the present state in the boom-bust cycle. In a boom cycle, the negative side of the distribution is inflated, in a bust cycle, the positive side is inflated. Compared to VaR, buVaR is countercyclical (it leads crashes), distinguishes between long and short positions (is asymmetrical) and provides an additional buffer for fat-tails by recognizing that crashes can happen only in the counter-trend direction. Thus, this method is useful for the purpose of a countercyclical capital buffer for market risk.

The approach relaxes the VaR assumptions of i.i.d. and stationarity of variables. It postulates that empirical phenomena of fat-tails, skewness, volatility clustering and the leverage effect, can be better understood by modeling the noise and cycle components together, instead of just the noise of the time series as modeled in VaR..

Full version available at SSRN: http://ssrn.com/abstract=1627674
or, CLICK HERE to download in PDF
Credit BuVaR: Asymmetric Spread VaR with Default
  Journal of Risk Management in Financial Institutions, Vol 5(1), 86-95
Author: Max Wong
A tradeable credit instrument shows two forms of credit risk—a continuous spread risk and a discontinuous default risk. The Basel market risk framework requires the two risks to be modeled separately for the purpose of regulatory capital but this gives rise to issues of risk aggregation. We propose a risk metric called credit bubble VaR (Cr. buVaR) that combines these dual risks under a common historical simulation value-at-risk (VaR) approach. By using a single model, Cr. buVaR bypasses the problem of risk aggregation. Credit risks can then be aggregated with market risk in a diversifiable manner. Cr. buVaR is also found to be forward-looking with respect to issuer credit default and is not procyclical.

The model is motivated by evidence from the 2008 crisis that issuer defaults and spread movements exhibit asymmetry, and that defaults are always preceded by rapid spread widening. The method involves scaling the positive side of the return distribution of credit spreads in proportion to current spread levels. By drawing inferences from studies on the “credit spread puzzle”, we deduce that the incremental loss of Cr. buVaR over spread VaR is due to default risk.

Full version available at SSRN: http://ssrn.com/abstract=1627689
or, CLICK HERE to download in PDF

         A longer explanation of some of the ideas of this paper and empirical results are available in the author's book "Bubble Value at Risk: Extremistan & Procyclicality" (2011).

Views expressed in this paper are those of the author's and do not necessarily represent the views of any organizations that the author is affiliated to.

Keywords: VAR, countercyclical capital, buffer, BIS, buVaR, bubble value at risk, Basel III, risk measurement, procyclicality, extreme events, market cycles, time series analysis


Wong, M. (2011)  'Value-at-risk, market risk models and Basel III', Risk Management, Oct. Issue No. 15, Tianyi Academy of Risk Management, Beijing (Chinese).
(Presented at The Fifth China Financial Risk Management Forum, Beijing (May 2011)). DOWNLOAD

‘Bubble Value-at-risk: a new tool for risk management’ -- Public Lecture, Singapore Management University, Singapore (Sep 2011).
Powerpoint  DOWNLOAD

RISKMIND$ Asia conference, Singapore (Sep 2012)
'Bubble VaR-- a Countercyclical Value-at-risk approach' -- abridged article  DOWNLOAD
'Have we waved goodbye to VaR' -- presentation  DOWNLOAD