2.5% probability of failing to meet return threshold

  • 2.5% probability of failing to meet a return threshold may be acceptable for many clients.
    • For normal distribution of returns, the probability of a return that is more than 2 st dev below the mean or expected return is ~2.5%
    • So if we subtract 2 st dev from a portfolio’s expected return and the resulting number is above the client’s return threshold, the client may find the resulting portfolio acceptable. If it is below, the portfolio may be unsatisfactory.
  • If client is more risk averse, you can choose a larger number for st dev. If client is less risk averse, choose smaller number.

Why is the bolded part true? This is from the book. If client is more risk averse, shouldn’t you want to choose a smaller number for st dev? You want there to be less chance of a negative return, and smaller volatility.

It’s creating a worst case scenario. If you show a risk averse client a larger standard deviation, resulting in a larger potential loss given the 2 standard deviation approach, they’ll say no thanks.

If you show a lower standard deviation you may risk “anchoring” their downside at that level. Thus you’d end up with an upset client when the market declines more than you indicated to them. Manage expectations.

That makes sense when looking at the client’s portfolio only.

But the statement in bold was made in context of comparing the client’s required return against a list of possible portfolios. If you increase st dev, then there are more portfolios available for the risk averse client. If you decrease st dev, then there are less available for the risk seeking. This is the opposite of my intuition.