Tuesday, March 14, 2006

Hedgers and Speculators

I was wondering if there was a specific combination of buy/selling a call or put that meant hedging or speculating. In other words, is there some reasoning that if like you buy a put or sell a call is always hedging or does it depend on the person's reasoning for doing what they are doing?

It usually depends on the specific situation. I think the best thing you can do to understand this is to read the solution to the problem on problem set 2 that dealt with this concept. Basically, if you have a number of investments, you need to think about whether they move in the same direction (i.e. you would profit on all or lose on all) or if they are uncorrelated (you will profit on some and lose on others). If it is the first case, one is acting as a speculator, and if it is the second, a hedger. A hedger wants to mitigate risk while a speculator wants to take on risk in hope of a high return.

Saving vs. Investment

I know S=I, but saving and investment aren't exactly the same. What is the big difference?

The difference is that saving is what households and the government does when they have more income than consumption. (i.e. they save what they do not consume) Investment is what firms do when they buy capital (or what households do when they buy homes) Households and the government supply loanable funds by saving, while firms (and households) demand loanable funds for investment.

Alpha Explanation

What does alpha stand for in the Y=A+aK+(1-a)L equation? Will it be given to us (unless its a problem where we need to solve for it)?

a represents the share of output (income) that goes to owners of capital. It should be given to you. If it is not given to you you can assume it is 0.3 I believe.

Bond Yield Question

I was wondering if you could explain bond yields to me. I'm a little confused as to exactly what they are. I was used to thinking of it as the interest rate that you would get on a comparable asset, but in the helpful hints it talks about a Wall Street Journal table and it talks about how different bonds have different yields. So what exactly is a bond yield, and how does it differ from a coupon payment?

Simply put, the yield on a bond is the value of i that makes the PDV calculation work out for the given price. It is also the yield on a comparable asset since efficient markets enforce the idea that returns on comparable assets must be equal.

In general, different bonds have different yields because they are not actually comparable. Consider the following situation- would you be indifferent between holding a 5% coupon Delta Air Lines bond or a 5% coupon General Electric bond, if they were the same price? (I use this example because Delta is performing poorly and filing for bankruptcy protection for the 800th time) If you would not be, then the two bonds are not comparable. Because Delta has a higher default risk, you would need to be compensated for that in order to be willing to purchase the bond. The way you are compensated is through a lower price, or equivalently, a higher yield.

If a bond is trading at face value, the yield is equal to the coupon rate. However, the coupon rate is stated as a percentage of face value, so it never changes. On the other hand, yield moves around as the price of the bond changes. Consider a bond that never expires with a 5% coupon. If the bond is trading at $100, you clearly get 5% return per year. If the bond is trading below $100, say at $90, you are actually getting a yearly return of $5/$90, which is greater than 5%. Thus your yield goes up. The opposite is true if the bond is trading above $100. (I use the consol example because then I don't have to worry about the return of the face value complicating the yield calculation.)

Don't forget...

2 important things to go over before your exam, since we didn't have time to fully cover them in the review session:

-- Helpful Hint on option pricing
-- Chapter 28 on unemployment (at least the main points)

Thursday, March 09, 2006

Financial Leverage

In general, financial leverage results from having control over an asset (read, getting gains and losses from) an asset that you don't own (yet). I'll give you the two examples that I gave in section:

1. I own a condominium in Harvard Square. This condominium cost about $400,000. If my property value increases by 5%, I realize a gain of 5% of the entire value of the condo, or $20,000. However, I did not pay $400,000 up front for the condo, I instead made a down payment and took a mortgage on the property. Thus I have control over the asset that I don't yet own outright. Say I put down $20,000 on the property. Then the 5% property value increase that I mentioned would actually be a return of 100% on my initial investment. Generally, financial leverage is characterized by higher percentage gains and losses than owning an asset outright. (If property value dropped by 5%, I would realize a 100% loss on my initial investment)

2. Say you have $500 to spend on financial assets. There is a stock that you are interested in that is trading at $50, and call options on this stock (with a strike price of $50) are trading at $5. Therefore, you can either buy 10 shares of stock or 100 options on the stock. Say the price of the stock goes up to $60. If you own the stock, you make $100, or 20% of your investment. If you own the options, you make $1000-$500 (the cost of the options)=$500, or 100% of your investment. Conversely, say the stock drops to $40. If you own the stock, you lose $100, or 20%. (This is only a loss on paper technically unless you are actually forced to sell the stock.) If you own the options, they are worthless (assuming they expire today) and you have a loss of 100% of your investment.

Wednesday, March 01, 2006

Efficient Markets and Stock Price

Q: Consider a stock that has an equal chance of being $27, $33, or $36 on, say, June 1st. What do you expect the price of the stock to be today?

A: To an approximation, an approximation which is sufficient for the purposes of this class, you can say that the price of the stock today must be equal to the expected future value. So the current price would be $33. This of course ignores the discounting that should take place from now until June 1st, and it doesn't incorporate a premium for uncertainty, but it is fine as an approximation.