Thursday, October 9, 2008

Rethinking the short sentiment on USD...

Leveraging refers to the simple act of borrowing X USD on the basis of the collateral of Y USD, such that X >> Y. So, X/Y = m refers to the leverage ratio at play. This ratio is assumed to be "stable" over the life time of a trade. However, as the net value of Y as measured in the market reduces, the leverage factor m increases. It is clear over the past year or so, banks have been actively involved in an effort to deleverage. The consequences are unclear in the long run - however, there seems to be emerging consensus that the aftereffects of this are likely to be significant. The effects of this reduction in leverage in the FX market is particularly interesting and complex. The order of complexity is furthered by the squeeze in the credit market. While the sentiment on the US economy is remarkably short -- the question regarding the USD is more complex.

One, particular confluence of credit and FX markets is the freeze up in the lending markets. In a fine essay by Thomas Stolper and others - they hint at the mechanics and the consequences of this relationship. Most banks have short dated FX obligations and longer dated domestic currency obligations. As the overseas short term lending markets freeze -- we get banks scrambling to find assets to pay out their obligations. Since most central bank lending mechanisms only lend in their domestic currencies -- most banks are forced to borrow domestically, convert that into the foreign currency and payout. The dollar denominated debts are the highest in the world, followed by Euro denominated and so on. So, as the US lending market freezes - one should the rising demand in the USD (as counterintuitive as it might seem).

However, this is one piece of the puzzle. The trader is only concerned with the net flow of dollars and changes in value - however, it is important to keep in mind the market imperfection (frozen credit markets) work its way through structural constrains.

Sunday, February 24, 2008

Falling Slowly

Historically, monies have been backed. Typically by Gold; occasionally by a basket of commodities; in more recent times to the value of another base currency. When asked what is the base currency backed by, since 1972, one could say "it's turtles all the way down".

i.e., Modern money is backed by only goodwill of the issuing government and the value that we, the holders, deem it to have. In the past, money was backed by commodities. Cowries, gold, oil, wood , slave girls etc., The Great British Empire was run on backed gold -- of varying quality -- backed by an asset, nevertheless. Since 1945-- the USD which has been the de facto currency of the world. On the extreme de jure currencies might exist but nevertheless be virtually ignored -- as in say, Afghanistan under the Taliban. Alongside, the key historical aspect is there has often only been a single de facto currency, on average, since the Enlightenment. Even the Nazi Germans during the forward stashed away their currencies in GBP.

What is peculiar about past four years is the following. We have two major currencies backed by nothing. And it seems increasingly clear there are two competing de facto currencies. The USD and the Euro. While the two currencies have had differing changes in value relative to other currencies over the past year (and more). See two cool graphs here: Euro & USD. The US is a behemoth with a cashflow problem; the Euro is essentially confederate money in a continent with a demographic problem. (See an interesting paper on confederate money.)

Now, the critical problem is globally: what is the optimal holding between USD and EUR. No ones the answer. In fact, one doesn't know if this is dichotomous choice itself is a false one. Increasingly, there are two other alternatives. Holding Gold itself. And as well, the basket of non-USD and non-EUR currencies. These are tough questions - but one thing is clear. The times have changed -- and we are, perhaps, entering for the first time since 1700s into an era of financial history that isn't very well known or even how to frame the questions correctly.

My own understanding of all this, on a weekend of Oscars, is more or less summarized by the preface to this song...

Thursday, February 21, 2008

Some Mortgage Basics

Last entry was on Nov 30, 2007. Now that I have gotten myself settled, and a rhythm in life has returned -- I should probably be in a position to post more frequently.

At the heart of the present crises that we are three factors: (i) default fears (ii) draining of liquidity (iii) industrial downturn. What has most gotten attention in popular press is default fears -- with default in household mortgages that has captured popular imagination. It is important to thus get briefly acquainted on how mortgage defaults (MD) are understood in most pricing or analytics.

MD is defined, in general, as when both of the following events occur: (i) unable to pay 3 consecutive monthly payments (ii) the equity in the home diminishes to leave no prospects of refinancing. Further, MD rates have a following shape. At first they rise, and then really spike up and then they decline -- graphed over years of mortgage existence.

Typical mortgages made out in the subprime market have been adjustable rate mortgages (ARMs) -- where the coupon is fixed for a while and then begins to reset periodically. Even the 30 year ARM in the regular markets are "5 x 1" (fixed for 5 years, and resets annually). In contrast, the 30 year ARM in a subprime markets are "2 x 28" (fixed for 2 years, resets semiannually for the next 28 years). Typically this reset is based of some pre-agreed index that tracks the cost of money, conditional on borrower quality, across the economy. So, if the generic interest rates begin to rise in the economy -- associated payable rates by the mortgage borrower are reset at a higher rate. What makes things worse is that most of these ARMs have an early "interest only" feature. Resultantly, as the "interest only" period finishes off -- the mortgage borrower has to start paying off for the principal component as well.

One of the critical issues every mortgage lender worries about is the prepayment of the lent amount. Typically, most of the pricing is done with some sort of prepayment model. The prepayment is a function of (i) available refinancing (ii) housing turnover (iii) curtailments (paying more every month than obligated) (iv) defaults. Typical modeling efforts of prepayment are applicable to a tranche of loans. As opposed to modeling prepayment for each loan.

Another layer of complication is to wonder about how to model the extent of loss that occurs as a mortgage defaults.

Now imagine writing securitized tranches that are sold which contain slices of mortgage backed securities -- i.e., CDOs on MBSs. It is not surprising then that we end up having this situation.

In essence, things get hairy pretty fast...

Friday, November 30, 2007

Top Recommendations by “the most profitable Bank”

Recently, following recommendations have been provided:
  • Long Ringitts, SGD and Taiwanese dollars – all funded by USD.
  • Sell pound-sterling against yen.
  • Sell gold.
  • Borrow in CAD, GBP, USD and buy BRL, RUB, CZK.
  • Sell 10-year CAD bond futures and receive fixed on 10-year CHF swaps.

Tuesday, November 20, 2007

How the "Masters of the Universe" think about Exchange Rates!

In a recent excellent, if perhaps deliciously short, report issued by the most profitable bank this year entitled "The Foreign Exchange Market" -- one of the sub-reports attempts to forecast the exchange rates for the coming year. What struck me about it is -- other than the predictions they make (I have my issues with that... see below) -- is the elegance of the underlying method. The way do is as follows:
  1. Changes in Terms of Trade (= price of exports divided by price of imports) is a function of changing commodity prices (energy, industrial metals, agriculture, live stock).
  2. Extract sensitivity estimates (the coefficients in a regression) to predict terms of trade.
  3. Changes in Real Exchange Rates ( = price of one unit foreign currency in domestic currency * ratio of foreign and domestic price levels) is a function of two key parameters.
    • Terms of Trade
    • Relative productivity levels -- measured by, say, per-capita output per hour etc.,
  4. Perform regressions on #3, using #2 to arrive at new estimates for real-exchange rates.
  5. Convert real exchange rates into nominal exchange rates.
Amongst key predictions are USD-CAD = 1.10; USD-INR = 50.1. i.e., their model supposedly predicts that the the Canadian dollar is expected to depreciate from the present levels, and so is the USD expected to appreciate against the Indian Rupee. Since, they do not explicitly mention all the concerned control variables in the exchange rate attribution -- it is difficult to really validate their claims, even intuitively.

My own guess is that there are three key parameters that affect the short term exchange rate fluctuations:
  1. Global capital flows -- that chase the second-order effects anticipated changes in terms of trade.
  2. Changes in US deficits (budgetary and trade) -- this is particularly accentuated by the coming US electoral-cycle.
  3. Idiosyncratic events -- particularly emerging market macroeconomic instabilities.
So, I suspect their analysis are largely driven by "true" long term economic factors, while the intermediate fluctuations are more complicated beasts -- and therein lies, as Shakespeare writes, the rub.

Mathematics for Derivatives

Often while reading about financial derivatives -- a lot of terminology comes to fore. Some are financial while the more esoteric ones are often mathematical. This document has some of them. Probability(errors) = 1 almost.surely.

Friday, November 16, 2007

Risk in the Times of Reversal

Standard Black Scholes pricing assumes a constant vol. The underlying implication being that the logarithm of the returns is normally distributed – and thus contained in it, a constant standard deviation (the constant volatility). In the market, there are other factors are play – such as supply/demand, risk-premia etc., -- all that contribute to, what Keynes memorably called “animal spirits” in the option pricing market. Typically, if the market expects a greater likelihood of the underlying exchange rate to go past the strike, the calls on the currency tends to get priced more expensively than the puts.

An option on call USD–CAD put refers to the call on the USD and the put on the CAD. So, the holder of the option has the right to buy the USD (convert the CAD notional at a prespecified rate). Equivalently, the holder of the option has the right to sell the CAD at a prespecified rate.

A spot price of 0.97, i.e., one USD can be exchanged for 0.97 CAD; with a strike of 1.01 on a call USD-CAD put refers to the right to buy one USD in exchange for 1.01 CAD. Tersely, the spot is 0.97 and the strike is 1.01 with a CAD-put. On the expiry date if the spot prices are 1.00, then the buyer of the call (with say 101 CAD in his account) would not exercise his option to buy a USD at 1.01 CAD when he can easily buy the same USD at 1.00 CAD. In this example, the USD is anticipated to appreciate. So, the call option on the USD-CAD is evidently ‘worth more” than a corresponding put option. i.e., if an appreciation is anticipated the corresponding call is priced at a higher level. This supply-demand forces are not a part of the Black Scholes derivation. Since, most parameters are fixed – the only “tweak-able” parameter is the vol – or the implied vol.

A 25-delta call refers to a call option where the strike above the spot (thus an out of the money option). So, in the above – it is clear that a 25-delta call has different implied vol than a 25-delta put. The “25” in the above refers to the fact if the underlying exchange rate increases by 1, the corresponding the call option value rises by 0.25. So, to arrive at a delta-hedge a corresponding position has to be taken in the underlying. The market convention of 25-delta is agreed upon – as one that is sufficient to capture the expectations regarding changing underlying prices. Of course, you can have 10-delta, 50-delta and so on.

A risk reversal is thus, the difference in implied vols between, ceteris paribus, out of the money calls and out of the money puts. Quoted thus, a rise in the risk-reversals means that as the currency appreciates, the volatilities are likely to rise. Instead, if risk-reversal are quoted as put – call. Then a rise in risk-reversal refers to the fact that as currency depreciates the vols are likely to rise.

A useful example of the trade flow is as follows: (courtesy

Assume an appreciation of the USD against the CAD over the next 3 month period (mean-reversion??). 3-month 25 delta USD-CAD risk reversal of 0.15 -.28% at a vol of 8.5% means:

1. Buy the 25 delta USD call/CAD put at 8.65% and sell the USD put/CAD call at 8.5%. The trader shells out 0.15%. i.e., he is paying a skew-premium of 0.15% in anticipation of a USD rise.

2. Sell the 25 delta USD call/CAD put at 8.78% and buy the USD call/CAD put at 8.5%. The trader earns the .28% spread.

On option desks, rules of thumb Rule! So, to extract the implied skewness, it is pretty standard to (a) calculate the risk-reversal (b) calculate risk-reversal per-unit of ATM vol. Risk reversals.

The big challenge is what to do when appreciations have different vols than depreciations. If you know how to deal with that – then there is some money to be made and a heck-of-career to be had!