A funny thing about the top of a curve: it’s flat. This flatness leads to an interesting investment question: are you willing to give up some return to reduce the bumpiness of the ride?
The Flat Top
When you look at the geometric frontier as a whole and not just the top point by itself, a judgement call comes into play.
The top of the curve is flat
Move very, very slightly toward less volatility, and you find a portfolio with the same return.
Yes, we’re dealing with infinitesimally small amounts of “less volatility” to still receive the same return. But nonetheless, the top is “flat.” And even when you move off the top at bit further it’s still very nearly flat (I chose a very flat example chart).
We’ve already discussed the logic of investing left of the top because of errors in portfolio construction. Let’s leave that behind for a moment.
Now let’s contemplate if there are other reasons to move off the peak as well? Is it worth reducing the return by 0.2% to reduce the standard deviation by say 5%?
This is a hard question to answer. I’m not sure there is a “correct” answer. I’m 100% sure not everyone has the same “correct” answer.
The Whole Story is in the Curve
One of the best descriptions of this challenge I’ve found comes from a podcast discussion with Ralph Vince. I came across Ralph years ago while searching for others who held similar beliefs for investing as myself. He has built his career around “Kelly” based trading strategies.
Here is a short clip:
At first I was solely interested in the peak….And I’ve since come to realize the whole story is in the curve, the shape of the surface — and how we move about and position ourselves on that surface to satisfy whatever criteria we are looking to satisfy.
Ralph Vince
At the time I didn’t fully understand what he meant about “positioning ourselves on the curve”. I was still focusing on the top. But I think I understand now.
Not Risk Aversion
Some may consider this risk aversion. Not really. There are mathematical reasons why an investor may desire this tradeoff.
As an example, drawdowns can potentially cause real problems for retired investors. Therefore a meaningful reduction in potential drawdown for a small reduction in returns may make sense for a retiree.1 It will reduce the chance they run out of money if the markets goes south for a bit (often called sequence risk). Pension funds can also face similar challenges.
Ralph speaks about “horizons” and “satisfying criteria”. He’s not talking about feelings, fears, or aversions. It’s about meeting the investor’s tangible requirements and goals.
Along the Curve
The peak is very important. It identifies the most aggressive portfolio an investor should aim for. It marks the rightmost point on the geometric efficient frontier (a limit which doesn’t exist in the efficient frontier). In a world without errors, it’s also the best return we can achieve.2
But then you realize the top of the geometric frontier is flat. The tradeoff between less volatility (less drawdown and less pain), and realized return is extremely low at the peak. Therefore does it make sense for some people to move off the peak for personal reasons?
For some I think it does. Therefore, how far down the curve do you move?
This is a question that I think about all the time. It’s where the really, really, difficult challenge in portfolio construction lies.3 It’s less dependent on math — it’s no longer as provable. It’s about you and your preferences, needs, desires, and goals.
Simply, it’s about the most difficult challenge of all: understanding yourself.4
1-Interestingly, the opposite is also arguably true. Steady income into an investment portfolio, can lead to a justified acceptance of larger drawdowns and increased “risk” in order to receive extra return..
2-Without leverage in these examples.
3-I’ll discuss ways to address this challenge in future posts, but first I needed to introduce the concept.
4- On a similar note, I have a theory that investing styles are really just an expression of self for the investor. Just as the car you purchase often comes from an expression of your personal values and identity (you relate with the brand), an investing style is also an expression of the investor’s personal principles and beliefs.
Do you think your approach could be used to identify a superior basket of stocks?
I mean, you could just use an index, but is there a way to pick a basket of stocks using the same features (return, volatility, etc) such that when you rebalance, you are picking the best stocks for the portfolio?
I think so, but it’s much harder to predict the arithmetic returns of individual stocks, and this should make the math trickier.
What is scale in your portfolio? Thanks. Keep up the good work!
It’s pretty much leverage, but I added it because it can help show how “safe” the current portfolio is, not to be used as leverage signal.
A higher scale is good. This lets people see a bit of what’s happening around the portfolio positions inside the calculations. When it falls, the strategy is getting “scared” and this happens sometimes even without any changes in portfolio composition.
Why didn’t you mention Sharpe ratio here? Does Sharpe not work the same when you’re looking at geometric returns (I feel like it should)?
A good way to decide your point on the curve would be to compare its Sharpe ratio with other portfolios
Sharpe ratio uses the arithmetic return, so no, it doesn’t care about the geometric return. The next post, “Kelly Investing is About Slope” may get to your point as share is really just the risk return slope.