Black Scholes N(d1) & N(d2) Explanation

For all the crazy mathematical types who love to look into the details...

In practical trading world, the delta of the option is taken to mean the probability that the option finishes in the money. Here, Professor Nielsen (currently at Columbia) provides a great write-up describing the difference between d1 and d2 under Black Scholes. Try to hold back your excitement!

https://docs.google.com/file/d/0B_RJrlEektmCbmdncVhka1FJa1U/edit

Zara - Honorable Mention in the World of "Relative Value"

Here at our blog Relative Value, we try to apply good risk/reward thinking to everything, not just investments! Clothes are fair target too because some are cheap and some are expensive. And working in finance puts a dent in your wardrobe because sadly in certain situations appearances matter. All in all, it's not easy to fit into a workplace where the Europeans are wearing vests underneath suits (that's right, these vest-sporting guys are in a financial firm, not at bar serving shots).

Now, let's focus on a store called Zara. Last year, the founder Amancio Ortego made headlines by supplanting Buffett on Forbes list of Wealthiest Billionaires:

http://www.bloomberg.com/news/2012-10-31/ortega-tops-buffett-with-zara-fortune-of-53-6-billion.html

The Bloomberg article above actually gives some decent background on the company's strategy. The whole idea behind Zara is amazing, they basically wait and see what are the fashion trends. Then when specific apparel become in fashion, Zara copies the styles which are in vogue for quick mass production. Hence you have very trendy clothing at reasonable prices. Zara also has a much milder and humble cousin, named H&M. Together, they bring cool to the masses. Fashion itself is a very interesting industry because there are no trademarks, patents, or proprietary information. Pharma companies patent their drugs to prevent competition, hedge funds attempt to maintain secrecy on their strategies to avoid sharing their pie with others. But in fashion, who's stopping someone from creating a similar product cheaper? So before you buy that cool shirt at Saks for $300, be sure to stop by Zara to see if there is a similar product. Of course, there are the exceptions like the Birkin Bag, which no one else could sell even if they could produce cheaply. 

Please note that Zara has a large sale, once a year in the summer (I'm not familiar with retail, so maybe everyone and their mom is having a sale in the summer). Like any risk manager who puts on size when the price is too compelling, be ready to stock up during the sales!

 

Emerging Markets Derivatives

Some insight into pricing and hedging emerging market derivative products.

Emerging Markets as Asset Class

Emerging markets can be thought of as a cross section of other assets in that it requires knowledge of many different asset classes. Let's illustrate this using a vanilla cross currency swap. When dealing with a cross currency swap in emerging markets, one must worry about many subtle differences from developed markets. For one, rates curves construction with special conventions (ACT/360, 30/360, etc). In addition, most emerging foreign exchange currencies are not deliverable. Lastly, there is an embedded credit exposure related to the cross currency basis swap.

Even within emerging markets, there are some regional differences. In Latin America, there is high product sophistication and strong external regulators. In Brazil, there is a large scope of exchange traded products. In the regional comprising of Middle East, North Africa, and Central Asia, one must consider special requirements, low products sophistication, and energy based economies. Lastly, Central and Eastern Europe is almost G10, yet still lack certain characteristics of developed markets.

Products to Model

There are many nuances in modeling different derivatives in emerging markets. Even in interest rate flow products, different conventions might throw off traders. While most traders in the United States are familiar with a 12 month calendar and intuitive conventions such as Actual/365 or 30/360, Mexican rate conventions required new calendars in risk systems. For example, the Mexican Basis Swap is quoted as 28 day basis vs. 1m USD Libor + Spread. Also, Real Rates UDI are quoted as UDI Fixed vs 6m USD Libor. In addition, Brazilian Interest rates are only calculated on business days. Interest only accrues on weekdays not weekends. This convention developed historically because Brazil rates were high and banks did not want to pay interest when they were not working. Also, one must consider other issues such as using DI Futures as the main IR curve building instrument or requiring model dependent Convexity Adjustment for Brazil CDI Participation swaps. In emerging foreign exchange markets, traders must be wary of extremely high volatility and cash settlement. Higher implied volatilities create challenges when calibrating models. In addition. onshore and offshore foreign exchange markets are related but not the same. Furthermore, certain currencies are pegged currency; the 2001 Argentine Default tested market models of pegged currencies. Lastly, inflation derivatives are special for most of Latin American countries as no such instruments similar to TIPS (Treasury Inflation Protected Securities) exist. Instead, the market CPI is implied by a discount factor on bonds.

Commentary

A former Latin America equity derivatives exotics summed up emerging markets with this thought: because the standards and practices of pricing derivatives in developed markets may not apply to Latin America, one must understand even the most basic pricing parameters. For example, in emerging markets, stocks may be difficult to short while at the same time difficult to also fund. Black Scholes assumes one can short assets and borrow cash at the same interest rate, but this spread between the rate of funding and rate of short borrow (repo) could be very wide on a Brazilian share. Therefore, the ability to manage the most basic functions such as funding and stock loan makes a large difference in managing exotic derivative positions in emerging markets. For example, the profit from trading exotic structures such as down-and-in puts can actually come from smart collateral management instead of smart risk taking on volatility.

Also, one must be careful when calibrating unusually high volatilities or extreme interest rates from market. In one experience I had, our firm modeled interest rates as continuous and represented them using an exponential function. While the daily compounded interest rate and the continuous interest rate are similar for normal interest rate levels, for unusually large interest rates, the daily compounded interest rate and continuous rate start to differ by a wide gap. During an unusual rate environment, the continuous interest rate implied by our model did not represent correctly the actual overnight rate to fund an instrument. Hence, for both developed and emerging markets, it is essential to firmly understand the mathematics behind pricing models and to question outputs which are out of line.

Introduction to Leverage and Banks

Summary of Balance Sheet

Fundamentally, Assets = Liabilities + Equity. The assets each have risk factors associated with them. With respect to liabilities, the simplest example of a liability is debt but for financial institutions, customer deposits are also liabilities. Leverage is defined as riskiness of portfolio with the simple explanation being that one can lose more than their Equity; here Hindy defines leverage as maximum loss. Leverage can magnify the magnitude of both losses and gains. The last concept is liquidity, defined as how fast can you transform an asset to cash. In general, traded securities are most liquid while private investments or real estate are illiquid.

In financial markets, most investment companies will mark to market their assets, which means at the end of the day, the value of the assets are marked to the current market price. They must do this because shareholders, lenders, and regulators need to have an accurate depiction of the company's value.

For a leveraged institution, if there is a drop in asset values, there will be an even greater decrease in the value of shareholders equity due to leverage. Sometimes the drop in value is so extreme that the institution needs to sell assets or raise equity to be compliant with risk limits or regulation. This initiates a vicious cycle where the institution can potentially fail. In Cypress, banks invested deposits in risky assets such as Greek Bonds, which fell in value, thus wiping out the equity and some deposits. In the United States, the government enacted deposit insurance, where banks pay a small premium each year to insure their deposits.


Systemic Institutions

Regulators can designate certain banks, insurers or even funds as "systemically important." To illustrate, Long-term Capital was an example of a systemically important institution. The fund required leverage in trading their arbitrage strategies in order to increase returns since each arbitrage trade only captured a very small spread. When LTCM was near failing, the Federal Reserve asked banks to inject equity into the hedge fund and slowly wind down positions. Else, the action of unwinding the funds positions could cause a significant disruption in financial markets since banks might hold similar positions as well.


Are Banks Well Capitalized?

One topic always up for debate is whether or not financial institutions mark to market their assets accurately. Certain U.S. banks (for example Bank of America) still trade below book value while having normalized yearly earnings of $2/share, leading value investors to point out that the value of their assets and loans might be inflated. In a past quarterly letter, David Einhorn of Greenlight theorized that the Fed wanted to create the current environment where banks slowly earn returns in order to bolster capital because certain banks might not have enough equity to withstand losses if they truly marked their assets to current market. This also explains the Fed’s yearly Comprehensive Capital Analysis and Review (CCAR) process whereby the government decides whether banks are well-capitalized enough to return extra capital back to shareholders in the form of buybacks and dividends. While most banks want to be able to pass CCAR in order to impress upon the market that they have strong balance sheets, regulators also want to make sure that banks have enough capital to withstand another crisis.