In an accompanying technical article we demonstrated important portfolio properties in the presence of shorts. We introduced a simple portfolio with $1000 invested in each of 3 stocks, namely: GOOG, AMZN and NFLX and $250 worth of FB short.
Then we wrote a simple script using our API to gradually increase the amount of FB short (keeping longs constant at $3000) and measured the marginal contribution to total risk (MCTR) from longs vs. shorts and systematic vs. idiosyncratic.
We presented plots that corroborate the behavior a portfolio manager might expect from the increase in shorts, namely:
- Overall portfolio risk decreases
- The amount of risk in the longs decrease and in the shorts increase
- The amount of systematic risk decreases and idiosyncratic risk increases (less and less can be explained by macro factors)
This behavior happens up to a certain amount of FB shorts, when it starts to revert itself. We contended in the article that PMs should understand these subtleties to achieve an optimum amount of shorts. For a detailed analysis, please refer to the article.
Whereas part 1 was concerned with MCTR, measuring the marginal contributions to total risk in normal times, this article will concentrate in the left tail risk during more extreme scenarios.
Left tail risk is also called Conditioned Value at Risk (CVaR) or Expected Shortfall (ES). It measures the expected profit and loss (PL) in low probability, high impact scenarios. We will measure those left tail risks in 2 different scenarios, namely:
- Technology ETF (represented by XLK) moving sideways
- XLK down 2%
Our API can efficiently perform these stress tests by perturbing a set of probabilities to satisfy the scenario shock. The technical details are beyond the scope of this article, but for now just imagine that the system can put more emphasis in scenarios that XLK is down 2% (for example). Because the total probability has to remain 1, it needs to reduce probabilities from other scenarios. The calculations are very complex and executed in a few seconds in our servers.
Scenario A) XLK sideways
The x-axis in the graph above depicts the amount of FB short in the portfolio, increasing from $250 to $10000 short (the long exposure is kept constant at $3000 and margin increases proportionally to keep constant leverage). The y-axis depicts the 5-percent worst PL from the 3 longs (in blue) and FB (in green). The sum of the 2 represent the total portfolio tail risk (in red).
The leftmost point in the plot ($3000 of longs and $250 FB short) shows that the portfolio left tail risk is -6.80%, whereas -7.30% is coming from the longs and +0.50% from FB short.
As FB short increases (x-axis), the left tail behavior has 3 important inflection points, namely:
- At $1475 FB short, the blue line crosses the red, indicating that 100% of the tail risk behavior is due to the longs only.
- At $2445, the blue line intersects the green indicating that both longs and shorts contribute the same to the left tail. The portfolio has the least amount of tail risk (4%)
- At $3919 the green line intercepts the red, indicating that all the left tail risk is due to FB
Next, we change the scenario to a shock on XLK of -2%:
Scenario B) XLK down 200bps
Contrasting this plot (XLK down 2.0%) with the one before (XLK sideways) shows very different behavior. The red line starts at a lower point here, i.e. the CVaR is -9.0% rather than -6.80% before.
Additionally the green line (FB) never goes down. Before, on a sideways XLK scenario, there are still many positive outcomes for FB causing the shorts to still contribute to left tail risk. With a larger XLK drop, correlations become stronger and there is less uncertainty about how longs and short contribute to the portfolio tail risk. In this scenario the shorts are very effective and the portfolio tail risk will quickly converge to the contribution from longs. In other words, there is small probability of FB contributing to a large downside PL (FB will add primarily to the positive outcomes).
Above, we plotted the contribution from longs and short to the left tail risk for 2 scenarios for XLK, sideways and down 2%. Below, we replicate these scenarios but decomposing left tail risks by systematic and idiosyncratic components.
Scenario A) XLK sideways
The axis are the same as before, x-axis represents the amount of FB short and y-axis is the CVaR. Red line represents the portfolio, blue is the contribution to CVaR from systematic sources and green from idiosyncratic.
The leftmost red point is the same as before, when we decomposed the left tail by longs and short, i.e. -6.80%. The contribution from idiosyncratic sources (green) is -4% and from systematic sources (blue) is -2.8%.
As we increase the amount of FB short the contribution from systematic sources to the left tail risk decrease quickly and become zero at $2800 short when the green line intercepts the red, i.e. the left tail risk is all due to idiosyncratic sources.
As we continue to increase the FB short, the contribution to systematic sources to left tail risk will slowly creep back into the portfolio (blue line gradually moving lower).
Scenario B) XLK down 2%
The above plot represents a scenario with XLK down 2%. In this scenario correlations are stronger and FB short is very effective. At $2880 FB short, the contribution to left tail risk from systematic sources goes to zero. The left tail risk quickly converges to pure idiosyncratic.
In this article we detailed the behavior of a simple long-short portfolio of tech stocks to demonstrate how our API can be used to generate optimum risk configurations. We decomposed the sources of left tail risk from longs vs. shorts and systematic vs. idiosyncratic. Our API stores both decompositions in an efficient data structure that can be retrieved with a single call to our servers.