price of futures, options, etc.

Economics Economics Questions
1

I’ve never fully understood how these are priced. Take bonds for instance, the price of bonds is always inverse to the interest rates because you must buy bonds at a lower price to make money from the interest on the bond. But that is just a deduction from the definition of profit, not a deduction made from praexological categories like time preference.

So I want to ask not just how these things are priced but also how these prices reflect concepts like time preference -would any of you like to offer some help?

2

With regards to bonds, the price and interest rate reflect not only time preference but also risk. If a company needing investment on a sound financial footing issues a bond, it’s price will likely be higher, but it’s interest rate lower. The investors know that the risk of their not having their monies returned from the investment is lower. From the initial offering, the price may go up because investors will likely see the benefit of a stable investment despite the lower interest rate for that investment. But, as more investors demand to purchase into the bond issue, the price rises and interest rate falls until the initial offering is completed. Afterwards, there may be swapping of assets (bonds for cash) on the secondary market as bond holders sell their holding to another interested investor. Conversely, a company on a shakier financial footing may not find as many interested investors. The price of the bond will go down to attract the attention of the investors, but the interest rate will also reflect the risk of investing in that company. The time preference would also be reflected in the bond’s maturity date–a short-term bond may have a lower rate than a long-term bond.

Options, futures, and forward contracts are a similar yet different sort of speculation. There is no interest rate on the instrument and the risks are greater, however; the return can be greater than a bond. As an example, I will use options. An option buyer has the right but not the obligation to buy (call option) or sell (put option) a specific number of shares of stock. Buying a call option would be made on ‘bullish’ speculation–regardless of how informed it is–that the price of the underlying asset will rise. Conversely, buying a put option is a ‘bearish’ speculation. The strike price is the key element in either investment. If the price of the underlying asset goes beyond the strike price (above for a call, below for a put), you are deemed to be “in the money”. When the option expires (typically the third Friday of the month) you can exercise the option and take ownership in the underlying asset. Or, you may sell the option contract at or before the expiration date. Sometimes, the options contract is more valuable than the underlying asset itself–as an anecdote, I found myself “in the money” on an call option I was holding for GM. I was able to sell the contract and make a decent profit for a small investment.

Which brings up another bit of information about options, futures, etc.: these forward looking contracts allow you to control (at times) a sizeable asset for a fraction of it’s cost. This allows for some people to profit off of fluctuations in the market that would otherwise be outside their financial ability. (I took a $200 investment in a call option and turned it into a little more than $1,000. If I had tried that with that particular companies stock, I would have needed roughly $15,000 for the initial investment and would have increased my positions value to a little more than $17,500.)

A great site for information is Yahoo! Finance. Another site I like to follow is Seeking Alpha.

I hope this info helps!

ricarpe

3

You can usually use the Black-Scholes model or the binomial pricing model to find the price of derivatives.

4

I understand most of what you’re saying but I still have residual questions. The most important though, is how is it that low interest rates and high bond prices don’t attract more bondholders to raise bond prices even higher while lowering interest even lower? Would this not mean that bond markets are the only markets where prices don’t really go down (except for the effects of exogenous events -a war makes people fearful to invest in bonds and their price lowers which limits investment funds encouraging higher interest)?

5

I’ll admit that my exposure to the bond market is limited to my short time actively working in the financial field–I spent two years working at a retail bank while I finished my undergrad (which involved savings bonds, CDs, and money market accounts) and one year after graduating university working for an investment company, dealing primarily with annuities (with bond funds available to investors). From my understanding of it, though, most bond investors are looking at the rate of return on the instrument they’re buying; that, and if the return on the investment isn’t greater than the return they could get from a similar instrument. I know that they normally will not accept an interest rate lower than they can receive by depositing the money in a bank and earning interest in that manner, usually from a money market fund. They are, after all, looking to make a profit.

Is it possible to have a 0% bond? Yes. If I remember correctly, one of the government bond auctions this past fall was even at a negative interest rate of 0.5% (although I don’t remember if that was the real or nominal rate). How a zero-rate, or even a negative-rate, bond would work honestly doesn’t make sense to me. The only thing that could make an instrument like these profitable is to use it as a hedge against rising inflation rates which would drive the real interest rate even further into negative territory than the rate on the bond. On the reverse side of that, if real interest rates stagnate or rise the investor ends up losing money. In essence, they end up paying money to loan money to the company.

6

The interest rate acceptable to any potential lender is based on time-preference and a risk component. Based on the interest rates acceptable to the different potential lender, and the rate that potential borrowers are willing to pay, one ends up with a nominal market rate of interest.

The risk-component can be broken into the risk of inflation, the risk of loss of partial or full default (“credit risk”), the risk that the market rate will change while one is tied into the term of this particular bond (“interest rate risk”).There is also the risk of a bond being “called” (where a borrower can effectively cancel the loan after a certain duration). In today’s world, there could also be currency-risk if one has the option of dealing in bonds that are denominated in various currencies. One can probably list other risks too.

The price of the bond reflects this aggregate market interest rate. Typically, a bond also has a face value and pays a rate based on that face value. These face-value (or “par value”) figures explain the inverse relationship of a bond and its market interest rate.

Example 1: Consider a bond of face value $1000 which pays $100 each year (10% of face value).

Suppose the market interest rate for this type of bond (for this “bundle of time-preference and risks”) is 5%, i.e. people who lend $1000 to a bond of similar risk are paid an interest $50 a year. Clearly, this bond, paying $100 a year, is worth more than $1000, since the lender gets $50 over the typical market return each year. So, it will sell at a premium to its face value.

Example 2: Consider a bond of identical risk and identical face value of $1000, but which pays $25 each year. This bond, paying just half of what the market expects, is worth less than its face-value of $1000. Though the lender will get back $1,000 at the end of the term of this bond, he is giving up $25 each year while he holds it.

If one knows the face value, the interest payment, term of the bond, and the acceptable interest rate it is a mechanical calculation to compute the acceptable price. The really difficult part is the judge the various risks and arrive at the correct acceptable interest rate. This is where opinions will differ.

Example 3: Finally, imagine that the market valuation of time-preference and risks changes. Imagine that now the market rate for these types of bonds is 15% ($150 each year, on $1000). Now, the bond in Example 1 is worth less than its face value. The market interest rose, and that bond therefore became less attractive. This is the sense in which the price of a bond is inversely related to moves in the interest rate.