BLSH Model - the Duality Case

When we let cash and risky assets change at the similar ways, we can observe that the cash asset (blue line) and risky asset (red line) move up at the similar rates. We call this case as the duality case because the dual (the cash and the risky asset) are moving together.

As we compared the total assets curve (green line) with the SPY (brown line) curve, we can observe the difference between them. The difference is expanding during the bull market; the difference is shrinking during the bear market. The two curves almost converge together during the worst time in the market from mid-2002 to early 2003.

Now the question is whether the two curves will converge again in the future. If they will converge, are there still incentives to hold the risky asset alone? I can not be fully confident to predict such a convergence. But I do understand the following insights based on this result.

(1) Holding risky asset is taking risks. At the same time, holding cash along is taking another kind of risks. It might be the two extremes in the case of duality can compensate each other in the long run with the minimum oveall risk.

(2) Market timing will add tremendous values if one can really do it correctly. If one can sell the risky asset when the price is high and buy it back when the price is low, he is becoming the guru of investment vey soon.

(3) If one realizes that he can not do market timing well, the duality case might be a balanced way to invest for the long run. Once in while (might be as long as 10 years), you will catch up with the guys who invest only in risky assets.