IMO the ulcer index is the best measure of volatility that matches what people intuitively care about. It essentially measures the frequency and severity of drawdowns (the linked page explains it in more detail).
I didn’t discuss the ulcer index in this post because in theory, investors with isoelastic utility should care about standard deviation, not drawdowns, and I lean toward the belief that people’s focus on drawdowns is somewhat irrational (although probably somewhat justified by the fact that most asset returns are left-skewed). But broadly speaking, if you use the ulcer index as your measure of risk, concentrating in a small number of assets looks even worse than if you use standard deviation, so the case for diversification is even stronger.
My thinking is that donating during drawdowns might be particularly bad, both personally and for your longer term donation strategy, since you’re selling low and “locking in” large losses in your portfolio. So minimizing drawdown allows you to better plan your budget and donations, and allows you more flexibility in timing your donations. You might find a particularly good donation opportunity during a drawdown period that will only be available during that period, but it’ll be extra costly (personally and to future donations) to donate then, so avoiding such drawdowns seems like an especially good thing to do.
Also, Sharpe penalizes extreme upside compared to Sortino, which seems weird to me.
Is it actually the Sharpe ratio that should be maximized with isoelastic utility (assuming log-normal returns, was it?)?
But broadly speaking, if you use the ulcer index as your measure of risk, concentrating in a small number of assets looks even worse than if you use standard deviation, so the case for diversification is even stronger.
My thinking is that donating during drawdowns might be particularly bad
This is true, and the standard deviation fully captures the extent to which drawdowns are bad (assuming isoelastic utility and log-normal returns). Increasing the standard deviation is bad because doing so increases the probability of both very good and very bad outcomes, and bad outcomes are more bad than good outcomes are good.
Is it actually the Sharpe ratio that should be maximized with isoelastic utility (assuming log-normal returns, was it?)?
Yes, if you also assume that you can freely use leverage. The portfolio with the maximum Sharpe ratio allows for the highest expected return at a given standard deviation, or the lowest standard deviation at a given expected return.
IMO the ulcer index is the best measure of volatility that matches what people intuitively care about. It essentially measures the frequency and severity of drawdowns (the linked page explains it in more detail).
I didn’t discuss the ulcer index in this post because in theory, investors with isoelastic utility should care about standard deviation, not drawdowns, and I lean toward the belief that people’s focus on drawdowns is somewhat irrational (although probably somewhat justified by the fact that most asset returns are left-skewed). But broadly speaking, if you use the ulcer index as your measure of risk, concentrating in a small number of assets looks even worse than if you use standard deviation, so the case for diversification is even stronger.
My thinking is that donating during drawdowns might be particularly bad, both personally and for your longer term donation strategy, since you’re selling low and “locking in” large losses in your portfolio. So minimizing drawdown allows you to better plan your budget and donations, and allows you more flexibility in timing your donations. You might find a particularly good donation opportunity during a drawdown period that will only be available during that period, but it’ll be extra costly (personally and to future donations) to donate then, so avoiding such drawdowns seems like an especially good thing to do.
Also, Sharpe penalizes extreme upside compared to Sortino, which seems weird to me.
Is it actually the Sharpe ratio that should be maximized with isoelastic utility (assuming log-normal returns, was it?)?
Makes sense.
This is true, and the standard deviation fully captures the extent to which drawdowns are bad (assuming isoelastic utility and log-normal returns). Increasing the standard deviation is bad because doing so increases the probability of both very good and very bad outcomes, and bad outcomes are more bad than good outcomes are good.
Yes, if you also assume that you can freely use leverage. The portfolio with the maximum Sharpe ratio allows for the highest expected return at a given standard deviation, or the lowest standard deviation at a given expected return.