Masters of the crayons

A pandemic introduction

I like to keep to myself; the pandemic made it clear that socializing has become more of a chore than a hobby. The sad (or maybe good?) thing is I couldn't tell you the last time I went to a bar. Long gone are the days when servers would know that if I wasn't 50 dollars deep into a bar tab by 2 PM on a Friday, something had gone terribly wrong on the desk. Nowadays, I do what I can to stay busy; a lot of it has come in the form of random pandemic activities, the most recent of which is an excessive obsession with ripping espressos and lattes. The addition of a puppy has kept me entertained and forced me out of the house, which is objectively a good thing. With the weather starting to improve, in the sense that I'm not dripping sweat plopped on my deck, I've been spending more time outside writing these explainer series. After all, it's time for me to get caught up on all those lost promises for further details in previous market updates.

I talk to my neighbors occasionally; it's hard not to when you have a dog under a year and an unfenced backyard. Most of the time, there's a monotonous exchange about "puppy problems" and how training and socializing are key to getting a well-balanced dog. Although I try to avoid it (just kidding, I live for the crazy), sometimes the conversation shifts towards global events and financial markets. The topic du jour ranges from vaccine conspiracy theories to my neighbor's insider stock picks. Naturally, I entertain these conversations, but I let my neighbors do all the talking for the most part. When the dialogue gets too intricate, my dog usually has to have his lunch/dinner, if you know what I mean.

In any event, I value these exchanges because it gives me an idea into what the average person thinks about world events. These conversations also emphasize how there have been real winners and losers from the pandemic. For example, while I've trained myself to wake up 10-minutes earlier to make a latte that a barista would have charged me $8 for pre-pandemic, my neighbor has been learning to draw squiggly lines on charts to inform investment decisions. There's nothing wrong with the latter per se, but a simple crayon drawing won't capture plenty of nuances you need to know to avoid getting steamrolled. Of course, the investment decision should also always be a function of the risk someone is willing to take or, put another way, how much someone can afford to lose. Unfortunately, those calculations are often overlooked by newly minted day traders who have stumbled out of the pandemic, some in worse shape than me out of the bar on a Friday night when life was simpler.

With that in mind, this post will focus on the concept of risk budgeting and how we can use this to explain the swelling disconnect between today's economic fundamentals and asset prices. Of course, I don't expect average investors to be well versed in risk management practices. Even within the financial profession, most fundamental/discretionary investors seem to turn a blind eye to the realities of risk management in a "lower for longer" world and the potential market impact these practices may have. Although it is not my intention to make everyone fluent in financial doublespeak, I hope to explain enough to help everyday folks understand the forces in financial markets.

Plug n play

Traditionally, investors have approached portfolio construction by allocating money to assets based on their expected returns and volatility. This approach involves a trade-off where the investor tries to maximize their returns while minimizing their risk. The optimal portfolio often involves a few heavy brains getting together and solving an optimization problem to get the best possible portfolio with the minimum amount of risk. Once we know the portfolio, where here I mean the assets and the amount we own of each, we can then plan to periodically rebalance these portfolios back to the optimal targets depending on how each investment performed over the period. This technique is known as capital budgeting and one classic example of the above is the 60/40 portfolio, which carries 60 percent in stocks and 40 percent in bonds. These two assets work particularly well because stocks and bonds are negatively correlated and tend to insult the portfolio from shocks in the market. The chart below shows how combining stocks and bonds can change the risk/return characteristics.

The chart shows that we can increase return without increasing risk by combining stocks and bonds up to a certain point. The colors on the graph represent the amount of return received for each unit of risk taken, measured by the annualized standard deviation of returns, AKA the Sharpe ratio. I don't want to get too caught up in the details here; the bottom line is that a portfolio manager will create a graph similar to this one and decide portfolio weights based on the required return and risk. This approach is known as capital budgeting since the portfolio manager allocated a specific dollar amount to each asset. Interestingly, we can see that the 60/40 portfolio doesn't maximize the Sharpe ratio in this particular data set, and that's because investors typically want a higher return than 5 percent per annum.

The portfolio that does maximize the Sharpe ratio is also the portfolio that equalizes risk contribution. In most portfolios that tilt towards equity exposure, most of the risk, if not all of it, comes from the equity side of the allocation. In English, this means that bonds are not adding any additional risk to the portfolio but are removing risk since stocks and bonds tend to correlate negatively. As such, portfolios with the highest risk-adjusted returns tend to have a bond weighting which is a lot higher than the 40 percent in the 60/40 portfolio -- usually around 75 percent bonds. With such a high weight to bonds, the portfolio's risk-return characteristics improve, but given that bonds are generally less risky than stocks, the overall return of the portfolio is less.

Risk budgeting makes momentum traders out of the best of us.

The approach described in the last paragraph is an alternative to traditional portfolio construction known as risk budgeting. Here, the investor starts with "risk budget," or the amount of risk they are willing to take in each asset in the portfolio. The portfolio manager can then solve the asset weights that keep the portfolio in line with the risk budgets. The risk budgeting approach may seem similar to the procedure above, but there are key nuances that result in vastly different outcomes. The main benefit of risk budgeting is that it prevents allocating too much risk to a specific asset or a group of correlated assets. In practice, this approach is much more complicated to implement and is done mainly by hedge funds, pensions funds, and other sophisticated investors. However, one benefit of executing this strategy is that it tends to outperform traditional portfolio approaches. Part of the reason for this outperformance is that risk budgeting has similar dynamics to momentum trading.

Risk budgeting can create herding effects, wherein lower prices can lead to forced selling which pushes prices even lower. To get an idea of what is going on here, I think it's helpful to start with an example. Imagine you have 10 dollars to go to the store and buy apples. If the price of apples is 2 dollars, you can buy five apples. However, if the price increases from 2 to 10, you can only buy one apple to stay within your budget. This same dynamic happens with a risk budget; as an asset's risk increases, a portfolio manager will need to hold less of that asset to meet their risk budget. Unfortunately for financial markets, most risk estimates revolve around an estimate of volatility, so as prices move in large swings, risk tends to increase. That shouldn't be surprising; if you're investing in an asset whose price is very stable, the odds of you losing your lunch money are low. The chart below shows estimates of volatility for stocks and bonds over 1-month compared to their daily returns. What's interesting to note here is that when asset prices move in any direction gradually, volatility tends to decrease, while large moves lead to significant increases in volatility. Also note that the axis are different for stocks and bonds. Bonds will have a lower volatility than stocks.

Now, of course, many things are going on here, but one key implication from this chart is that risk budgeting practices force asset managers to mechanically sell into falling/rising markets when the moves are significant. Now meaningful price increases matter less from a market stability and functioning perspective because asset managers are selling into surging markets and are providing liquidity. I know there's a lot in that sentence so lets take some time to unpack it. Since prices are increasing, there are likely more buyers than sellers in the market. Thus, the cost of having risk budgeting strategies selling in these markets is relatively low since they are insulating the market from further increases and creating a more balanced order flow. Remember that for asset managers to stay within their risk budgets, they must be selling when volatility increases. Where things get a bit dicey is to the downside, where, using the same logic above, if prices are falling, there are likely more sellers than buyers. Thus, risk budgeting strategies actively remove liquidity by selling into already falling markets, potentially exacerbating market corrections.

It's all about those flows.

The dynamic described above is in contrast to the one seen in traditional portfolio allocation. While under a risk budgeting approach, investors behave more like momentum traders during periods of turmoil by selling into falling markets, traditional portfolio construction tends to do the opposite. For example, under a conventional portfolio construction approach, assets that have performed well over the period will be sold and replaced by those that have relatively underperformed. This dynamic ensures that the weights derived from the optimization of risk and return are maintained. The chart below shows the relationship between buying/selling during rebalancing periods relative to the performance of the asset.

Unsurprisingly, we see that there is a negative relationship between returns and the changes in allocation. Moreover, we can see that the relationship is more deeply negative for equities than bonds, likely because equities are more volatile (take a look at the first chart).

Under risk budgeting, the story changes. To illustrate this, we will use a unique case of risk budgeting known as risk parity, where we set 50 percent of the total portfolio volatility to both equities and bonds. Of course, the above is just shoptalk for having a 50% risk budget for each asset. The chart below shows how risk parity allocation changes with the performance of the underlying assets during the rebalancing dates.

We can see that the relationship now flips positive and is far less tight. Moreover, here we can see that these strategies are trading similarly to momentum, as lower prices tend to lead to selling and lower allocations. The lack of diversity within the investment industry related to risk management leads to these commonalities across systematic investing strategies, which are critical mechanisms for propagating shocks throughout the financial system. These commonalities can also help explain why asset prices may deviate from fundamentals. The current market environment has volatility approaching historic lows, which leads to more buying from systematic investors that use volatility as a toggle for position sizes. The chart below shows how the simple risk parity strategy I used in the example above has been slowly building exposure to the equity market.

As is the case with most things I bark on about, there are many subtleties to consider, many that merit a separate post which I will likely write when I start doing deeper dives into specific systematic strategies. This post served as a brief introduction to risk budgeting and tried to tackle some of the more pressing issuers about the potential systematic implications of the widespread use of risk budgeting. There's a lot in the post, and I make some leaps that may not be easy to follow. If you have any questions, please feel free to reach out.

Thanks for reading,

Tiago Figueiredo