Risk of ruin

Risk of ruin is a concept in gambling, insurance, and finance relating to the likelihood of losing all one's capital[1] or impacting one's bankroll to the point that it cannot be recovered. For instance, if someone bets all their money on a simple coin toss, the risk of ruin is 50%. In a multiple-bet scenario, risk of ruin correlates with the number of bets, in which risk increases the longer one plays.

Finance

Risk of ruin for investors

An investor with no liabilities and all their assets in gold has zero risk of ruin, but they forgo earning opportunities and unless there is a sustained and substantial rise in the value of gold, their relative wealth may decline.

Two leading strategies for minimising the risk of ruin are diversification and hedging. An investor who pursues diversification will try to own a broad range of assets – they might own a mix of shares, bonds, real estate and liquid assets like cash and gold. The portfolios of bonds and shares might themselves be split over different markets – for example a highly diverse investor might like to own shares on the LSE, the NYSE and various other bourses. So even if there is a major crash affecting the shares on any one exchange, only a part of the investors holdings should suffer losses. Protecting from risk of ruin by diversification became more challenging after the financial crisis of 2007–2010 – at various periods during the crises, until it was stabilised in mid 2009, there were periods where different assets classes became correlated across all global regions. For example, there were times where both stocks and bonds [2] were falling at once – normally when stocks are falling in value, bonds will rise, and vice versa. Other strategies for minimising risk of ruin include carefully controlling the use of leverage and exposure to assets that have unlimited loss when things go wrong (E.g. Some financial products that involve short selling can deliver high returns, but if the market goes against the trade, the investor can lose significantly more than price they paid to buy the product.)

The probability of ruin is approximately

P(\mathrm{ruin}) = \left(\frac{2}{1+\frac{\mu}{r}}-1\right)^{\frac{s}{r}}

where

r = \sqrt{\mu^2+\sigma^2}

for a random walk with a starting value of s, and at every iterative step, is moved by a normal distribution having mean μ and standard deviation σ and failure occurs if it reaches 0 or a negative value. For example, with a starting value of 10, at each iteration, a gaussian random variable having mean 0.1 and standard deviation 1 is added to the value from the previous iteration. In this formula, s is 10, σ is 1, μ is 0.1, and so r is the square root of 1.01, or about 1.005. The mean of the distribution added to the previous value every time is positive, but not nearly as large as the standard deviation, so there is a risk of it falling to negative values before taking off indefinitely toward positive infinity. This formula predicts a probability of failure using these parameters of about 0.1371, or a 13.71% risk of ruin. This approximation becomes more accurate when the number of steps typically expected for ruin to occur, if it occurs, becomes larger; it is not very accurate if the very first step could make or break it. This is because it is an exact solution if the random variable added at each step is not a Gaussian random variable but rather a binomial random variable with parameter n=2. However, repeatedly adding a random variable that is not distributed by a Gaussian distribution into a running sum in this way asymptotically becomes indistinguishable from adding Gaussian distributed random variables, by the law of large numbers.

Financial trading

The term "risk of ruin" is sometimes used with a relatively narrow technical meaning by financial traders, to refer to the risk of a trading account becoming "ruined" in the sense that it's not allowed to make further trades. Sometimes its possible to precisely calculate the risk of ruin for a given number of trades. For example, assume one has $1000 spare in an account which one can afford to draw down before the broker will start issuing margin calls. And say each trade can either win or lose, with a 50% chance of a loss, capped at $200. Then for four trades or less, the risk of ruin is zero. For five trades, the risk of ruin is about 3%, as all five trades would have to go bad for the account to be ruined. For additional trades, the risk of ruin slowly increases. The calculations required to evaluate the risk become much more complex with realistic conditions. To see a set of formulae to cover simple related scenarios, see Gambler's ruin. Opinions among traders about the importance of the "Risk of ruin" calculations are mixed – some advice that for practical purposes it is a close to worthless statistic, while other say it is of the utmost importance for an active trader to be aware of it.[3][4]

See also

Notes and references

  1. ↑ "Risk of Ruin (Forex Glossary)". Financial Trading Journal. Retrieved April 26, 2012.
  2. ↑ Though US treasuries were generally an exception, except on the very worse days their value generally rose, as part of the "Flight to safety".
  3. ↑ Trading Risk: Enhanced Profitability through Risk Control Kenneth L Grant (2009)
  4. ↑ The trading game Ryan Jones (1999)

Further reading

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