Risk of Ruin (Probability of Ruin)

Risk of Ruin = ((1 - (W - L)) / (1 + (W - L)))U

Where:

• W = the probability of a desirable outcome, or a win

• L = the probability of an undesirable outcome, or a loss

• U = the maximum number of risks that can be taken before the individual reaches their threshold for ruin

Also known as the probability of ruin, the risk of ruin is a concept that originated in the gambling industry but can also apply to investing. The risk of ruin is the probability that an individual will reach their point of ruin, which can mean the loss of all of their investment, or a large portion of it.

The most commonly cited risk of ruin example involves the toss of a coin. If an individual could lose all of their investment with a simple toss of a coin, their risk of ruin would be 50%. Another example is gold, which is considered a universally accepted means of payment. If an individual were to hold gold in safekeeping, their risk of ruin would be 0%. However, by keeping their funds in such a safe investment, they are forgoing the opportunity to earn a higher rate of return on their investment. Fortunately, investors do have the opportunity to lower their risk of ruin, and achieve reasonable rates of return, by using strategies such as assembling a diverse portfolio.

Historically, a trader conducts a successful transaction 52% of the time, and 48% of the time they lose the entire investment. In this example, the trader's total funds are $100,000, each trade involves $5,000, and the trader's point of ruin is $70,000. This means the maximum number or risks the trader can take before reaching their point of ruin is $70,000 / $5,000, or 14. The risk of ruin would be calculated as:

= ((1 - (0.52 - 0.48)) / (1 + (0.52 - 0.48)))14= ((1 - 0.04) / (1 + 0.04))14= (0.96 / 1.04)14= 0.923114, or 0.3261, or 32.61%

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