- Martyn Wild

# Portfolio construction: what's your favourite flavour?

Updated: Jul 25, 2021

By Martyn Wild.

**Vanilla ice-cream tastes okay, but its not for everyone**

Those in the business of constructing portfolios tend to rely on classical mean-variance optimisation as written about by __Harry Markovitz__ and focus on one particular metric as their objective function: minimising volatility (represented by standard deviation) for any given return. This is the ubiquitous 'Efficient Frontier'; the vanilla-ice cream, if you will.

Standard deviation, however, can only be an accurate reflection of risk if returns are normally-distributed and as we have shown in the past, market returns are decidedly *not *normal for most investments. As such, some people prefer to derive their efficient frontier by replacing standard deviation as their focus with metrics like downside-deviation (where they essentially minimise the standard deviation of only those returns *below *the target return). Others prefer to minimise left-tail risk by using conditional value-at-risk (CVAR) as their objective function. But we believe that the issue is much deeper than whether or not standard deviation is the right thing to optimise.

So is there an alternative to vanilla ice-cream when constructing frontiers? In short, we think so.

**Chocolate-chip cookie dough, anyone?**

In our experience, clients rarely ask their adviser to minimise volatility. They do however often make a point of highlighting their heightened sensitivity not achieving their goals. As such, we think that it is critical to build sensible portfolios that maximise the likelihood that the investor will achieve their investment goals. We refer to this measure as the *Success Factor.*

In the chart below we present two frontiers:

where

*standard deviation has been minimised*for any given return (orange line)where

*Success Factor has been maximised*for any given return (blue line)

Both frontiers are derived from identical data and use up to eight asset classes, where there are no restrictions on the amount that is allocated to each asset (other than they must collectively sum to 100% and each have a weight between 0% and 100%, inclusive).

Superficially, they look very similar in return/risk space. In fact, they are *so *similar, its difficult to see the frontier that has been built to maximise the Success Factor. So in the chart below we show the difference in volatility between each frontier, i.e. how much more volatile each portfolio is when optimised for Success Factor.

We've purposely zoomed-in so the differences are clear, but note the scale on the y-axis: the biggest difference in volatility between the two frontiers is less than 7 basis points! The frontiers are essentially the same in return/risk space. Nevertheless, what do we get for these minor differences in volatility?

In the chart above, we illustrate the difference between the frontiers when we consider Success Factor. In all instances, the Success Factor frontier is equal to or better than the frontier that is optimised on standard deviation. In many cases, the Success Factor frontier is able to improve the likelihood of achieving the target return by more than 3.5%! That's material.

When it's not uncommon for portfolios to offer lower than a 50% chance of achieving the target return over the shorter term - essentially a coin-toss - a 3.5% higher chance is important. If you're interested in seeing the two frontiers in return/Success Factor space, take a look below.

As you can see, where Success Factor has been optimised, the blue curve is always to the right of the traditional frontier for the same return. If you are wondering why the curves are not smooth, that's essentially due to the non-normality of the probability distributions of the optimal portfolios.

**What's your favourite flavour?**

So do we think that building a frontier based on standard deviation is a bad idea? Of course not. Frankly, it's a solid start that often approximates to the optimal solution. However, we firmly believe that investing is all about probability; not least, doing our level best to ensure the client receives the return they need with maximum certainty.

So whatever your favourite flavour of portfolio construction, our suggestion is to at least try something new - if only to make sure that you're happy with what you currently have. There's way more to life than sticking to vanilla.

For more information or to talk to a member of the MARQAM team, please click here.

*MARQAM is a privately-owned, boutique consulting company focused on providing superior investment outcomes for clients and greater profitability for businesses. We are not affiliated with any other financial institution*

*Disclaimer: The information provided here is for interest purposes only and does not constitute investment advice or a recommendation of any kind.*