[veeenu]

This is widely known among practitioners, but there is a caveat -- a 1/N portfolio bears a much higher risk than, say, a cap-weighted portfolio or a risk-parity asset allocation. A 1/N portfolio receives an equal contribution in terms of volatility from each asset, meaning that very risky assets significantly increase the portfolio's volatility, while not necessarily contributing proportionally better returns, due to the nonlinearity and asymmetry of volatility's effects on prices. This way, 1/N ends up performing very poorly on a risk-adjusted basis while undoubtedly at the same time outperforming any other kind of allocation on the basis of return alone. This is rather unacceptable in a real world portfolio where the tail risks and emotions can lead an investor to ruin.

[OnlineGladiator]

> This way, 1/N ends up performing very poorly on a risk-adjusted basis while undoubtedly at the same time outperforming any other kind of allocation on the basis of return alone.

I fear I'm misunderstanding you. Are you saying despite having higher returns, the higher risk makes this strategy worse? That really feels like handwaving to me, since the only thing I care about is ROI. I understand nonlinearity and how it could tank your investment, but if it doesn't and you make more money then you're criticizing something that never happened. The higher risk is already baked into the ROI, because it includes the times that failed. The point is, in aggregate, you make more money - and most of the time that is the only thing I care about when investing.

Or am I misunderstanding you?

[veeenu]

You are not misunderstanding. While there is no doubt that there is a premium on taking more risk, ROI is also a very debatable metric to consider in a vacuum, though. If you only care about ROI then you either can afford to risk everything because you have cash/safer investments in place (so you are really taking less risk), or you are YOLOing.

> it could tank your investment, but if it doesn't and you make more money then you're criticizing something that never happened

This way of reasoning is basically survivorship bias in a nutshell, and per my direct experience as a financial professional has brought down many investors who were too confident about their "strategy".

To bring this argument to the extreme: if you cared only about ROI, you could just go long some penny stock with exaggerate leverage and make big money "unless proven otherwise". In practice, what happens is you get euphoric for a couple days while you see the money shoot up to the sky, and then lose all of it to a margin call at the opening the very next day. I've seen it happen with my own eyes.

[medvezhenok]

The reason that risk is important to quantify is because leverage could be used (in theory), to achieve risk parity between different strategies. So ideally you would pick the one that has the best risk adjusted returns (with enough diversification) and then leverage it to the amount of risk you would be comfortable with.

As a highly simplified, unrealistic example - let's say strategy A has an average return of 5%/year with max drawdown of 20%, and strategy B has an average return of 10%/year with a max drawdown of 50% (here max drawdown being a highly simplified proxy for risk). Theoretically, you could use leverage to go 2.5X long strategy A to achieve a return of 12.5%/year with a max drawdown of 50% (minus cost of the leverage - depending on how you do this, cost could be fairly small). This might do better, risk-adjusted, than just doing strategy B by itself.

[greg7gkb]

I think another way to characterize 'riskiness' is the volatility of a portfolio, IOW how much does it swing up and down over time. So everything else being equal, two funds with the same ROI may still have different levels of volatility, with the fund having the lower volatility being more desirable.

[bumby]

>Are you saying despite having higher returns, the higher risk makes this strategy worse? That really feels like handwaving to me, since the only thing I care about is ROI.

There’s lots of metrics that try to balance the risk and reward. Often, the risk is based on the volatility of the asset. The common alpha metric does this by incorporating the assets volatility compared to the overall market volatility. There’s others like Sharpe ratio etc.

Factoring that volatility is particularly important in long-term investing so your choices don’t, as you say, tank your investment. So maybe you interested in cyclicals over the last nine months and your investments went gangbusters. Does that mean that same strategy will work in perpetuity? Probably not, because cyclicals tend to have high volatility. Risk -adjusted metrics attempt to quantify that risk.

[Behemoth66]

I believe OP is saying that due to the increase in risk and volatility there is a greater chance of the trader to emotionally manage their money as it peaks and falls.

And obviously there’s mathematical measurements where one tries to get the highest return per unit of risk. It’s possible that these returns might be higher but fall under the curve.

[veeenu]

Addendum: the paper actually mentions the Sharpe ratio, which is a general, popular measure of risk adjusted returns, but which fails to take into account the non-normality of the distribution of returns; so, while my previous comment may be incorrect in a Gaussian world, I would be curious to see the results when the performances are evaluated under the assumption of fat tailed processes, which I presume would paint a very different picture.

[bumby]

Interestingly, low volatility investing has some studies that show it can provide better risk adjusted returns than naive 1/N allocation or traditional Markowitz optimization

[veeenu]

Yes! There is a number of widely known inefficiencies (low vol, mid cap stocks, the trend following anomaly, long volatility oriented strategies...) that consistently produce better risk-adjusted returns. Some of them aren't really popular enough to stand out and reach their full capacity, others (trend following especially) are so counterintuitive that in practice almost no manager nor investor ends up being able to sustain the emotional pressure, eventually everybody cries uncle and there is no way the anomaly gets crowded enough to go away.