Most of us can understand at an emotional level how people were feeling about the markets in September:  many of us were, for starters, incredibly nervous about the fate of financials.

• Lehman Brothers had declared bankruptcy
• Merrill Lynch was bought by Bank of America
• There were only two investment banks left in the United States!
  • Morgan Stanley in particular looked very vulnerable.
  • When Morgan’s stock dipped below 20, everyone was wondering “will they be the next one to go?”

Compare the collective sentiment surrounding Morgan Stanley in September with with how people were probably feeling about Coca-cola.

Coca-cola a soda company. Sure, perhaps people may drink less soda in a rough economic period, but since soda is so cheap and people don’t like to change their habits if they don’t have to, soda-drinkers will probably keep drinking soda for the next few years. Your 401(k) tanking? Your mutual funds worth nose-diving? The least you can do is treat yourself to a soda for lunch.

Compared to Morgan Stanley, emotions around Coca-Cola’s stability were certainly more calm, more subdued.

But these are just feelings — fear about Morgan Stanley, calm about Coca-Cola — what did the market think about this? How did the market display all of the emotion and fear and uncertainty we had about Morgan Stanley during the week of September 15th?

The answer is volatility.

First, two definitions:

Implied Volatility

• The volatility of an underlier as implied by the prices of its options
• Specifically, implied vol is the result you get of plugging the option prices into the Black-Scholes option pricing formula
  • Note: For the best layman’s explanation of Black-Scholes I’ve ever seen, read Emmanuel Derman’s My Life as a Quant: Reflections on Physics and Finance.  He compares Black-Scholes to the art of making fruit salad

Historical Volatility

• The volatility of an underlier as measured by past percentage price moves

I will focus on implied volatility.

As an exercise, let’s compare the volatility levels of Coca-cola and Morgan Stanley, for the ATM options that expire September 19th . . . (For both examples, I chose strikes closest to being at-the-money as I could)

Coca-Cola

On September 18th, the 52.50 strike September 2008 call contract, set to expire the following day, closed at $0.55.  Coca-cola stock itself closed at $53.39

Let’s use this information to calculate the implied volatility.  We’ll use the free Black-Scholes calculator available at http://www.soarcorp.com/black_scholes_implied_volatility_calculator.jsp

Input	Value	Notes
Call option price	1.35
Stock price	53.39
Strike	52.5
Interest rate	3.84%	Historical LIBOR available at: http://www.bba.org.uk/bba/jsp/polopoly.jsp?d=141
Time to expiration	1 day

Using the above inputs, the calculator tells us that on September 18th, the Coca-Cola Sept 2008, 52.50 Strike call had an implied volatility of 75.3% at the close

Morgan Stanley

On September 18th, the 20 strike September 2008 call contract, set to expire the following day, closed at $4.04. Morgan Stanley stock itself closed at $22.55.

Once again, let’s use this information to calculate the implied volatility.

Input	Value
Call Option Price	4.04
Stock Price	22.55
Strike	20
Interest Rate	3.84%
Time to Expiration	1 day

Once again using this calculator, we determine that on September 18th, the Morgan Stanley Sept 2008, 20 Strike call had an implied volatility of 584%

75.3% vs 584%! That is an incredible difference. But why are they different?

Let’s break down what each volatility number means.  Some things to keep in mind:

• Volatility is quoted in annual terms
• Volatility numbers refer to one standard deviation from the mean (i.e., they represent what we expect to happen 2/3 of the time)

Coca-cola – 75.3% vol

This volatility level means the market expects Coca-cola to go up or down . . .

= 0.753 * 53.39 (the close price of the stock)
= $40.20
. . . $40.20 or less 2/3rds of the time (this is over the course of one year)

In other words, one year from now, we expect to see Coca-cola trading between $13.19 and $93.59 2/3rds of the time.

We can also break this down to a daily price change expectation. This volatility level means the market expects Coca-cola to go up or down . . .

= (0.753 * 53.39) / squareroot(252) because there are 252 trading days in the year
= (0.753 * 53.39) / 15.874
= $2.53
. . . $2.53 or less 2/3rds of the time (this is over the course of one DAY).

Even these high implied volatilty numbers, though, are nothing compared to what we saw with Morgan Stanley

Morgan Stanley – 584% volatility

This incredible volatility level means the market expects Morgan Stanley to go up or down . . .

= (5.84 * 22.55)
= $131.69
. . . $131.69 or less 2/3rds of the time (this is over the course of one YEAR)

We can also break this down to a daily price change expectation. This volatility level means the market expects Morgan Stanley to go up or down . . .

= (5.84 * 22.55)/ squareroot(252)
= 131.69 / 15.874
= $8.30
. . . $8.30 or less 2/3rds of the time (this is over the course of one DAY)

What is incredible about this comparison is the difference’s between the two companies stock price.   Morgan Stanley closed at $22.55, but its 20 call option had a $8.30 up or down price move built into it.  Coca-cola, whose stock was $53.39, over $20 more valuable than Morgan Stanley, had only a $2.53 expected up/down move built into its 52.5 call.  Then again, Coca-cola wasn’t tottering of the brink of  insolvency on September 18th, 2008.