Problem

The text box Is It Surprising that So Many Commercial Mortgages Default? presents a simplified way to compute a rough estimate of the likelihood of mortgage default as a function of property value volatility and the LTV ratio of the loan when it is issued. There it was argued that a 75% LTV ratio lending criterion would lead approximately to a one-sixth lifetime default probability. Use this same simplified approach, and the fact that about 5% of the normal probability distribution lies beyond two standard deviations from its mean, to estimate what LTV ratio lending criterion would be necessary to reduce the default probability to 1/40 (or 2.5%).