Hedgers and Speculators

Q:
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?

A:
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

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

A:
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

Q:
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:
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

Q:
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?

A:
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)

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.

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.

US Holding of NYSE and NASDAQ equities

I just wanted to point out that most of the $14 trillion that we talked about in the NYSE and NASDAQ market values is held by US households (as opposed to internationally), either directly or indirectly. (Households can own equities directly by buying a mutual fund or depositing in a money market account, or buying stock of one company that has stock of another company on its books.)

Savings Institutions

When we talked about savings institutions (financial intermediaries) in class, I kept using banks as an example. This is not the only example of a financial intermediary- there are Savings and Loan companies, credit unions (I believe that Harvard employees have a credit union) and finance companies (such as GM's loan arm, GMAC). For our purposes, these instituions basically function the same as banks. Furthermore, banks are the most important (i.e. widely used) financial intermediary. The 15% figure I gave in class would be for all financial intermediaries, but banks make up the vast majority of that number.

Supplying Saving vs. Supplying Securities

I wanted to make an important distinction that I feel was not entirely clear in class. I will use an example with bonds, but you can replace stocks with bonds here and everything would still be correct. First, if you are SUPPLYING saving, you are actually demanding bonds. If you are supplying (also referred to as issuing or selling) bonds, you are DEMANDING saving, i.e. borrowing. Notice that the roles are reversed in depending on whether you are talking about loanable funds or financial instruments. I mention this because understanding the concept of selling vs. buying bonds will be very important later.

Convergence

In response to a student question from Barro's lecture:

There are actually two concepts in growth economics- absolute convergence and conditional convergence. The idea of absolute convergence is that there is one value of per capita GDP that all countries are growing toward (an equilibrium level if you will). Alternatively, you can think of this as poorer countries growing faster than richer countries no matter what, so that eventually they will all come to the same steady state level. Conditional convergence, on the other hand, postulates that there is a unique steady state level for each country. This level depends on things like natural resources, institutions and government frameworks in place, etc. If these are not present to a sufficient degree, the country will have a very low steady state and/or may not converge at all. Alternatively, you can think about convergence to steady state (and catching up to rich countries) is conditional on these things being present. With absolute convergence, a country with a lower GDP would be growing faster, since it has further to go to achieve steady state. With conditional convergence, a country that it further from its own steady state would be growing faster, and it slows down as it approaches this steady state. I don't know that the distinction between absolute and conditional convergence was explicitly made in lecture. The point is that being further away from steady state implies faster growth.

There are a lot of analogies that I could make here. My current favorite is Newton's law of cooling. My physics is a bit (read, very) rusty, but I seem to remember that if you take an object of one temperature and drop it into a substance of another temperature, it heats/cools quickly at first, since the temperature differential between the two substances is high, and then as the substance gets closer in temperature to that of its surroundings, it heats/cools more slowly. The process is described by a differential equation of the form dT/dt = k(T-T*) or something similar (again, rusty), which looks not too different from what you saw in lecture.

Definitions From Barro Lecture

I noticed in Prof. Barro's lecture that there were several acronyms that he used without (in my opinion) adequately explaining. So I will add some information here.

PPP: stands for Purchasing Power Parity. In context, Barro said that the Summers dataset for GDP adjusted for PPP. Let me give you an example of why this is useful. Normally, you could compare GDPs across countries by just using exchange rates to convert everything to US dollars. However, if you just do this you might notice strange things like the fact that a Big Mac would cost $10 in some countries and 15 cents in others. In other words, the purcahsing power of US dollars is very different in the two countries. The PPP just adjusts such that, at least on an aggregate level, the amount of stuff you could buy with a given number of US dollars would be the same for each country. It's a bit of an oversimplification, but you get the idea.

OECD: stands for Organization for Economic Cooperation and Development. I think I explained this very briefly last semester. Basically, a bunch of countries (mainly developed countries) realized that it would be helpful to understand the macroeconomies of other countries, so they formed this organization to share information and whatnot. You can learn more at www.oecd.org. This is relevant to you guys for now mainly because a lot of the cross country data that economists look at comes from here.

A Nasty Whiff of Inflation

I welcome you to ask questions about the above article from the first section. As Simon pointed out, the article can be confusing to you- I read it over again and realized that it talks a lot about concepts (monetary policy and interest rates for example) that you haven't learned anything about yet. I think the main gist of what you are supposed to be getting from this article is an example of what would cause inflation, or an increase in the CPI. The parts about loose monetary policy and such are still a little over your heads at this point, but not to worry!

Growth Rate Form of Production Function

Recall that in class I gave you the production function Y=Af(K,L), and then a couple of minutes later I gave you an equivalent equation in growth rates form, given by:

%chgY = %chgA + a%chgK + (1-a)%chgL

(I apologize for the abuse of notation, I'm somewhat limited in the characters I can use!) Some of you are likely wondering how on earth we can go from one of these to the other. So I will try to explain. Last semester I explained that a change in a variable (change in total cost for example) could be represented by the derivative of the variable (eg. marginal cost is the derivative of total cost). Now, a question for you: what is the derivative of ln(x)? It's dx/x, right? Or alternatively, the change in x divided by x. This is the definition of percent change, is it not? Thus, (instantaneous) percent change in a variable is the derivative of the natural log of the variable. Now, why is this useful?

In our discussion, we are assuming a particular functional form for the f function given above. Specifically, we are assuming what is called a Cobb-Douglas production function. This function is f(K,L)=(K^a)*(L^(1-a)) for some a between 0 and 1. So now you have Y=A*(K^a)*(L^(1-a)). To get the percent changes, take the natual log of both sides and then the derivative:

lnY = ln(A*(K^a)*(L^(1-a)))

lnY = lnA + ln(K^a) + ln(L^(1-a))

lnY = lnA + alnK + (1-a)lnL

dy/y = dA/A + adK/K +(1-a)dL/L (this is the total derivative since the terms are separable)

%chgY = %chgA + a%chgK + (1-a)%chgL

I hope that makes sense!