Alpha and Sailing

21 July 2006

By: Alpha Male 

This article (”Portable Alpha: Beta & Alpha, Both Important, Totally Different & Great Together“, July 2005) on combining non-correlated assets will resonate with sailors.  Ferrell and Podewils propose a method of analysing the benefits of diversification using vector analysis.  While they don’t specifically make reference to sailing, they use many of the same concepts.

“Risk vectors are a helpful tool in measuring Beta and Alpha risks and correlations.  The length of each line shows the amount of expected volatility. The angle created by the intersection of the two lines shows the correlation of their risks. If we observe the risk of a portfolio comprised of a combination of two perfectly correlated risks that are both long investments, the combined vectors are double the original volatility. Returns are also doubled, in both positive and negative directions.”

For sailors, one way of looking at Ferrell and Podewils’ approach is to view the volatility of the equity market as the wind direction where the length of the vector represents the annualized standard deviation of the market (e.g. S&P500) rather than the wind speed.  Let’s say the annualized standard deviation of the S&P500 was 20% and that your whole portfolio was made up of the S&P500 (e.g. via SPDRs).  Then let’s say you replaced half of your holdings with a fund that had a 1.0 correlation to the market.  Since the correlation is one, the volatilities would be purely additive and your overall portfolio volatility would remain 20%.  With a correlation of 1.0, you can never lower your volatility from 20%.  You are essentially on a “run” with the market.  This is illustrated in the chart at left.  (sailors: remember to flip the arrow directions to understand chart)  On a run, your complex and expensive sailboat is unable to add any value beyond a leaf being blown across the water. 

Now let’s say you liquidated half of your SPDR holdings and bought a fund with a 0.5 correlation to the S&P500.   This is illustrated by point “C” this chart.  As Ferrell and Podewils show, overall volatlity is not purely additive and there are benefits to diversification in this case since the resulting vector (or volatility) is shorter (or lower) than the “run” shown above.  This is analogous to a broad reach and implies that your boat is “adding value” beyond simply beng blown across the water like a leaf.

Using the same logic, a correlation of 0.0 implies a beam reach.  In a very real way, a beam reach does have a “zero correlation” to wind direction - for evidence, simply consider what would have if the wind direction was to shift 180 degrees: nothing.  The sails would simply switch sides and the boat would continue to travel in the same direction at at the same speed.

As we move up the sailing chart toward a close haul (call it, say, -.75) we are seeing more and more of the technical magic of a sailboat come into play.  In fact, those new to sailing are typically amazed to learn that a sail boat can sail towards the wind at all.  Similarly, those new to hedge funds are often amazed that you can make money in down markets (i.e. you can have a negative market correlation).  Both are amazing feats of technology that defy common sense.

But while boats can sail close to the wind, they cannot sail directly into the wind.  They must instead tack back and forth, zigzagging upwind on opposing close hauls.  So does our sailing analogy fall apart when we need to account for correlations of exactly -1.0 (such as Ferrell’s and Podewils’ example to the left)? 

Thankfully, the answer is “No”.  The sailing analogy holds up well in this scenario.   Remember that  two perfectly offsetting (-1.0 correlation) securities will guarantee zero return with zero standard deviation.  In other words, your portfolio would go nowhere if you liquidated half of your SPDR’s and shorted SPDR’s with the proceeds.  Your portfolio would just sit there motionless as if it were in irons.  And like a boat in irons, your portfolio will graduallly decay due to friction costs.  Before you know it, you attempt to sail directly up wind will take you back to where you began (or worse!) 

If this were not the case, an arbitrage opportunity would present itself and riskless profits would be possible.  This would be a fantasy scenario for investors: perfectly offsettings risks with a positive residual return.  The sailors upwind fantasy scenario is not very different: perfectly offsetting forces with a residual force moving the boat forward.  If only sailing and investing were that easy.  The bottom line is that you can’t sail directly upwind and you can’t make money by being perfectly negatively correlated with the equity markets.     

Students of sailing will recognize the further similarities between correlation and sailing.  When sailing upwind, the Bernoulli Principle creates a force on the sails that pulls the boat sideways.  Combined with the force of the wind itself, there is a force on the boat that is angled slightly forward, but is still mostly a sideways force (called the centre of effort or “CE”).  To compensate for the lateral force associated with this angle, the centreboard, daggerboard or keel provides lateral resistance (called the centre of lateral reistance or “CLR”).  Essentally, the centreboard cancels out most of the lateral drift caused by the sails driving forward at a very obtuse angle.  These opposing forces cancel each other out, leaving only a pure, albeit, much weaker, forward drive for the sailboat. 

When the wind gusts, the CE strengthens and the boat is forced even more strongly to the side.  But the centreboard (CLR) compensates by pushing even harder to keep the boat from sideslipping.  When there is a lull, the CE and CLR both weaken in unison.  So the CLR is a near-perfect hedge against the CE’s sideways drift.  What is left is pure alpha - a weaker, but consistant force that has been “distilled” by mitigating opposing forces.  It allows the boat to travel forward no matter which direction the wind were to come from or how violently it blows. 

All sailors face the same wind and all investors face the same market.  In both cases, skill is required to a) trim the sails in order to balance the angle and power of the CE (CE=the long portfolio) and b) manage the size and position of the CLR (CLR=hedge).

Upwinding sailing is all about balancing speed and angle.  A close reach might be faster than a close haul, but it will require more tacking to get from A to B.  A close haul, on the other hand, is slower, but is more steady and will likley reach point B as fast as a close haul, with less tacking.  Similarly, a tightly hedged portfolio that squeezes out 8% per annum consistantly might get you to the same place as a more volatile (less-hedged) portfolio producing 15% per annum because it rides all the gusts and lulls of the market.

- Alpha Male

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