Thursday, July 10, 2014

Fun With Market Probability Density Functions--Estimates of the Future Behavior of Asset Prices (or why dollar/yen is not going to collapse)

From Chelsea Global Advisors via Advisor Perspectives:

The Tide is High
It took a while but I think I finally get it.  The Federal Reserve has embarked on a Parallel Campaign [1] - operating on two separate planes that seemingly never intersect, yet both having readily recognized similarities.  My eureka moment finally came this past week when Ms. Yellen, in a rebuff to the Bank for International Settlements, said "because resilient financial system can (now) withstand unexpected developments, identification of bubbles is less critical."  What she means is that due to the vastly improved safety and soundness of the financial system, unorthodox monetary policies can remain in place far longer than perhaps previously deemed prudent, mainly because the overall system is now better insulated and can withstand unexpected shocks.  I believe this is the clearest indication yet that the FED is using both its regulatory authority and its ability to set interest rates to meet its statuary goals of maximum employment, stable prices and moderate long term interest rates.  Up until now, many observers, including myself, believed that rather working in concert, the two main arteries of the FED were pulling in opposite directions.  After all, some allegedly punitive regulatory measures, enacted to curtail a considerable amount of the more risky activities of banks and other financial intermediaries, could easily have hurt the real economy and capital formation.  Unmistakably, such an outcome would appear wholly at odds with the purpose and objectives of the rate setters at the FOMC since 2008.  Now for the first time, Ms. Yellen has specifically connected macro prudential regulatory policy with monetary policy.  It's a big deal. 

Overconfidence 
Most people that have closely monitored the expansion of the post crisis regulatory agenda will readily admit that large majority of the final rules and regulations that have been passed into law are as strict, if not stricter, than the original proposals.[2]  Despite countless objectives from industry insiders and lobbyists, the new laws designed to control and govern conduct offer few safe harbours or exemptions - and promise severe penalties for violations. 

Over the past six years, just about every senior banking executive and investment manager or trader that I have worked with has grossly underestimated the impact of the new rules and regulations on their businesses and on the industry and most were supremely overconfident that the rules could be easily sidestepped[3].  It's still going on.  Today, a similar mistake to underestimate the FEDs resolve to keep rates lower for longer and to be over confident in econometric models that suggest interest rates should be higher.  U.S. Treasury bonds had a bad week and 10y and 30y rates hit 2.65% and 3.47% respectively.  Both yields are likely to trend higher this week ahead of supply (reopening of 10s and 30s); however, I will have buy orders in 2.75% on 10y and 3.64% on 30y.

If the FED is following an optimal or even sensible policy is not at issue here.  All that really matters is that they believe they are - and if that's the case, then short term rates are likely to stay low for a very long time and the regulatory environment will get even more restrictive. The arrival of an unwelcome houseguest, such as unanticipated higher inflation, which is always a possibility, is surely the only obstacle that can force the FED to abandon its campaign.

Sharpen Your Pencils 
What happens when the spread between the implied or realized market risk premium and the risk free rate widens at the same time realized variance declines?  Geniuses are made - literally by the tens of thousands.  The math is simple and intuitive, yet striking.  For the past ten years the S&P has had a CAGR[4] of 6.67%, with a standard deviation of 17.56%.  During that time the average risk free rate was about 2%, proxied by the average 1y T-bill rate.  That gives a Shape Ratio of about .27.  That not great and it indicates that an investor had to take a fair amount of risk in order to earn between 6% and 7% on average.  Now assume the markets market risk premium has not changed (i.e. it is still 6.67%), but the risk free rate has dropped to just 10bp from 2% and the standard deviation of returns has decline to just 10% from 17.56%. Now the Shape Ratio has improved to .66 from .27 and improvement of 1.44x!

It's important to note here that I kept the market's risk premium static and only changed the risk free rate and the volatility assumptions.  Nothing really changed fundamentally in the economy, yet investors now seem to be masters of the risk-reward equation.  Shopping a high Sharpe Ratio to potential and existing investors is de rigueur in our business and is an absolute must when raising money for a new fund.  Today's artificially high Sharpe Ratios are poorly understood in my view and may lead to poor asset allocation decisions.  Your author would prefer to invest with a person who claims they can make 20%, with a risk free rate of 5% and a standard deviation of 30% (that's a Sharpe Ratio of .50) rather than with some who touts a .75 Sharpe Ratio based upon miniscule risk free rate and volatility assumptions. 

Forget Obamacare, Puts are Cheaper 
The price of a put option represents the product of the discount rate, risk aversion parameter and the probability of a decline in prices.[5]   We can observe the discount rate - its low, but not the risk aversion parameter (which is based upon personal preferences) and now thanks to the work of the Federal Reserve Bank of Minneapolis we can also extract the risk neutral probability of a crash (or huge spike up in prices) in certain assets classes.[6]   I intend to return to this theme at a later date and attempt to explain the theory, in layman's terms, behind some of the math.  For now, I will look at one tradable quantity, namely the dollar -yen exchange rate.
 According to the work done at the Minneapolis FED, the probability of a large change in either direction of dollar-yen is virtually zero at the moment.  No wonder FX volumes have collapsed so much!  For purposes of this exercise, a large move is defined as a move of plus or minus 10% from current spot prices.  The probability is extracted from the prices of actual traded dollar - yen FX options transactions rather than from some fancy model.  The results are called risk neutral probability densities. Take a look at the chart below. It shows the market's perception of the probability of large dollar-yen FX moves has collapsed, after spiking in the middle of last year during the market's taper tantrum.
 
Whether you applaud or denounce the policies of the FED and Bank of Japan, you have to admire their success so far at reducing uncertainty in the cross rate.  If victory is measured by reducing risk and uncertainty premiums, then by all means, today's central bank policies are wildly successful.  Luckily, their policies have also pushed down the prices of tail insurance, including puts, to unbelievable levels.  As the saying goes "It's totally irrational, but ultimately logical."

So when the tide rolls out, which even King Cnut failed to prevent, at least you will be left with some sand under your feet.  Buy some insurance....MORE 

Right now Chelsea is pretty much Mr. Talisse. Here's his bio at TabbFORUM.
Here's the Minneapolis Fed:

Market Probability Density Functions
Updated with data through June 12, 2014

Latest Report
June 12, 2014 [PDF]
Commentary Inflation
RNPD skew derived from inflation caps and floors moved higher and turned positive over the past two weeks at the two year expiry. At all expiries, risk neutral probabilities for inflation of less than 1% continue to fall indicating that the markets continue to assign less probability to lower inflation rates. Below we update the graph we published two weeks ago and note the spiking skew (red line) and declining standard deviation (blue line).
Chart 1
Banks & Insurance Companies
RNPDs derived from options on equities were largely unchanged across the 31 BHC and insurance company markets we follow. Options trading volumes were generally below average and statistics calculated from the risk neutral distributions showed only minor differences from two weeks ago.
The average CCAR 17 bank price change matched the average of 11 insurance companies price change equaling 2.9% over the past two weeks. This outpaced the S&P 500 price change of 0.50%. Average RNPD standard deviations for banks and insurance companies remain at multi-year lows signaling continued market expectations for low tail risk....MUCH MORE
And:
Estimates of the Future Behavior of Asset Prices