## Determining Probability of Ruin

This calculator provides an estimate of an investor’s, or gambler’s, risk of ruin (ROR), sometimes referred to as the probability of ruin. The calculator requires a total of four inputs, including:

- The amount of funds at risk
- The investor’s, or gambler’s threshold for ruin
- The funds at risk per transaction
- The probability of a win

Using this information, the calculator then provides the user with three outputs, including:

- The probability of a loss, which is the inverse of the win value
- The number of transactions until the ruin threshold is reached
- The risk or probability of ruin

### What is the Risk of Ruin?

Risk of ruin measures the likelihood of losing the total of an investment or the value of that investment dropping below the threshold for ruin. This concept applies in finance as well as in games of chance that involve gambling. The most common example of the risk of ruin is a fair coin toss, which is one that has a 50% chance of being heads or tails. In this example, the risk of ruin would be 50% if that person was betting up to or beyond their threshold for ruin.

In the finance field the investment could be shares of common stock, bonds or even real estate since these would all be considered liquid assets. Risk of ruin calculations also rely on the random walk hypothesis, which states the price of an asset, like the market prices of a stock, move according to a random walk. This means price changes cannot be predicted. So, if the initial risk of loss is 50%, each subsequent transaction has the same risk of loss. For example, if a coin comes up heads on the first flip there is a 50% chance it will occur again on the next flip. Investors can minimize their risk of ruin through hedging strategies in addition to creating a diversified portfolio of holdings.

### Interpreting the Results of Our Calculator

The results of our calculator are easy to understand and interpret. Using the default calculator values we see 1,000 as the funds at risk, while the threshold for ruin is 200. At 100 funds per transaction, we know there are exactly eight transactions before ruin is possible (1,000 – 200 = 800 /100 = 8). Since the win probability is set to 60%, the probability of a loss is 40% (100% – 60% = 40%). Given this scenario, the calculator tells us that after eight transactions the risk of ruin is only 4%. This low risk of ruin is primarily a function of the relatively high win probability.