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In game theory, a Nash Equilibrium is the solution to a non-cooperative game involving two or more players. It is further assumed that all players know the strategy of the others, while none of them benefit from changing their strategy unilaterally. The ongoing fiscal cliff showdown that is now running perilously close to pushing our economy into recession can be analyzed in this context to predict what outcome should be expected.

To analyze the current impasse, let us view Obama and the Democratic Party as one player in a potential Nash Equilibrium, while the Republican Party is viewed as the opposing player. Obama and his party have made their perspective on the showdown very clear. Obama's statement on Friday afternoon is an excellent summary of his position. He intends to allow taxes on high-income families to rise without raising rates on middle and lower-income families. Furthermore, spending cuts would be implemented in a manner consistent with his proposal. After winning the 2012 election, Obama clearly feels that he has a mandate, and his current proposal is consistent with stated planks in his re-election campaign.

Boehner and the Republicans have an equally clear strategy, which is: no new tax increases on the wealthy and corresponding cuts in government spending that are greater than what the president and Democrats are proposing.

John Nash's brilliant yet simple insight is to predict what decisions would be made by each party taking into account the other party's decision-making process. Imagine that each player asks themselves: "Knowing the strategies of the other players, and expecting that they cannot change should I change my strategy?" If any player answers yes, then the set of strategies is not a Nash equilibrium. If every player optimizes their strategy to achieve the best possible outcome assuming their rival's strategy is unchangeable, then we have reached a Nash equilibrium.

First, let us analyze what is the best outcome for either party. Both parties want their stated objective and both parties wish to avoid the fiscal cliff scenario. However, because the two parties have mutually exclusive goals, neither party can obtain its objective and avoid the cliff without the other party yielding. Thus avoiding the cliff is a question of whether it is more important to either party to avoid the cliff scenario by sacrificing their stated objective.

It is clear from watching Obama's statement that for him avoiding the cliff is not more important than sacrificing his position. In fact, his statement appears to insulate himself from the consequences of ongoing gridlock by placing the blame for the current impasse on Congress. While it is possible he simply wishes to appear ready to walk away as a negotiating tactic, it is likely that he is not bluffing. I expect Obama is correct in anticipating that the Republicans have more to lose in the present situation; thus going over the cliff is a win and having the GOP back down is a win. From Obama's perspective: even if the GOP's position is unchangeable, it would not change Obama's approach. Then the central question becomes: Are the Republicans prepared to sacrifice their goal of not raising taxes to avoid the fiscal cliff?

This question is central to how events will proceed. The Republicans need to balance the desires of their constituency against the odds that they will do themselves considerable harm by appearing culpable for the cliff scenario. From the GOP's perspective, if Obama's position is viewed as unchangeable, they should pick the better of two losing scenarios. Which is more important to the GOP? Avoiding culpability for the fiscal cliff or not sacrificing their stated objective of preventing tax increases on the wealthy? The downside from backing down appears much less than the downside for going off the cliff. Therefore, it is believed that the fiscal cliff impasse will reach its Nash equilibrium when the GOP accepts that the best course of action is to compromise. If the GOP compromises on taxes, we will have a Nash equilibrium, where each party gets a desirable outcome assuming the other party's strategy is set in stone.

Note that several assumptions have been made. First, it is assumed that there is still time for both parties to reach a mutually agreeable solution. Second, it is assumed that the Republican Party is not fragmented to the point that a unanimous judgment cannot be reached. Either of these assumptions proving untrue would render the entire argument moot and cause reaching a deal to be impossible.

Conclusions

In a previous post, it was put forward that avoiding the cliff would cause the market to rise to 1500, while falling off the cliff would cause the market to fall to 1330. However, at that time, I was speculating about the odds for reaching a deal by year's end. It is expected that an extended period beyond 1/1/2013 without a deal in place will cause the market to price in a recessionary scenario.

Based on last summer's crash, a recessionary scenario will cause a decline to 11x forward earnings, or approximately 1200 on the S&P 500. Previously, I advocated raising cash because at 1450, the market was pricing in an unrealistic probably for a deal. Based on the large sell-off in S&P 500 futures after the market closed on Friday, we now have implied odds placing a deal by January at less than 15%. At this point, the chance for a deal within only a few days is remote and it is likely that even an optimistic buyer of stocks should wait for a bit more downside yet. However, whether to buy around my 1330 target changes because the pessimistic outcome has become no deal and a likely recession, which will cause the S&P 500 to descend to 1200 in short order. Therefore, not reaching a deal now means a roughly 13.4% decline versus an 8.3% gain implying a 61% probability of a deal. From the analysis above, it seems logical to conclude that a deal should be forthcoming, making the wager seem reasonable.

If you also believe the Republicans will accept the better of two losing outcomes, then the time to buy stocks is near at hand. An S&P 500 index fund would therefore be a timely purchase after a bit more downside, essentially buying where the market sold off to in November (~1330-1350 - SPY). However, if you believe that the Republicans will not or cannot reach consensus, then the market is still not cheap enough for betting on a positive outcome.

In another week, Obama or Boehner believing that a deal is near or scheduling a meeting will not placate the market. The market will instead look to the impact of potential tax increases and spending cuts amounting to 3% of GDP and suddenly realize that recession is the likely outcome.

It is hoped that both political parties will be able to reach consensus; however, it is also recognized that hope is not an investment strategy. It is very concerning that this close to a deadline, both parties still refuse to reach some sort of deal. The possible outcome of this stonewalling is an overreaction not unlike last summer's market crash. Thus, while buying attractively priced stocks is beginning to make logical sense, the risks have increased substantially if no progress is made.

My advice at the current juncture is simple: if no deal is announced, sell any 'hope' fueled rally. When the Republicans accept the better of two bad outcomes, it will be a good day to buy stocks, including but not limited to: AFLAC (NYSE:AFL), Apple (NASDAQ:AAPL), Chevron (NYSE:CVX), International Business Machines (NYSE:IBM) and McDonald's (NYSE:MCD). The spiking VIX also means that selling puts will be an attractive measure once a bit more certainty has been established. The only stock above I would advocate selling puts on is AFLAC, for which you can receive over a $5 premium for a Jan-2014 50 strike put, creating a breakeven of $45/share if the put is executed or a return of over 10% if it is not. Selling puts on SPY can also be an advantageous strategy during a spike in volatility.

I must also emphasize that I do not advocate using your entire portfolio to 'time the market.' Instead, I advocate freeing up cash during good times in order to have buying power during market declines.

Additional disclosure: This article is apolitical and its intent is not to scapegoat either party, but rather to analyze the best course of action for both sides of the dispute. Please refrain from blaming either party in the comments section and instead agree or disagree with the articles conclusions.

Source: Approaching The Fiscal Cliff As A Nash Equilibrium