Why Portfolio Optimization May Exclude a Risk-Free Asset

# Portfolio selection with no risk-free asset


# Portfolio selection with no risk-free asset












Can someone explain why some papers on portfolio construction assume that there is no risk-free asset? For example, this paper: Machine Learning and Portfolio Optimization. What could be the reason(s) for this assumption of "no riskless asset"?

## Answer by kurtosis (score 2)

https://quant.stackexchange.com/a/58245

There are a few reasons the authors may have only looked at risky assets.

First, they are trying to find a faster way to solve a mean-CVaR optimization through relaxations. Therefore, they probably saw handling the risk (CVaR aka ES) as the most interesting part of the problem. Granted, doing so completely ignores that they should be looking at excess returns, but that is not their concern and would not render their approach incorrect. Essentially, they are not wasting time on getting into the argument about what is the risk-free rate and if it is truly risk-free in light of inflation.

Second: while most portfolio construction assumes there is a risk-free asset, we often build portfolios where we know there is not a risk-free asset.

For example, suppose you were building a portfolio for an equity fund in Argentina (or Russia or many other countries). Those countries have defaulted in the recent past, so assuming their (same-currency) government bonds are risk-free is a poor assumption.

However, Black (1972) says that we are fine so long as we can construct a zero-beta portfolio. If we were to update this for a multi-factor APT world, we need to be able to build a portfolio with all-zero factor betas. If we can do that, then we have a proxy for a risk-free (or as-riskless-as-possible) asset which we can use to compute excess returns.

## Answer by develarist (score 1)

https://quant.stackexchange.com/a/58226

They just want to apply their technique to risky assets that actually have volatility. The risk-free asset has a volatility of $0$ so allocation towards it is treated as an after-thought since it's pretty much in an asset class if its own, whereas the risky assets on the risky side of the portfolio might have to be allocated from various risky asset classes or sectors/regional groupings.

They are not saying the risk-free asset doesn't exist. They just want to address the risky side of the portfolio problem while excluding, or assuming away, the riskless asset for the particular demonstration at hand.