The capital market is an important mechanism and a key factor in producing economic growth and a stable economy. Financial markets transfer funds from people who have excess available funds to people who have a shortage. They promote greater economic efficiency by channeling funds from people who do not have a productive use for them to those who do. If we want to know how the capital market functions, it is important to understand how individuals make their investment decisions. Classical Utility Theory provides the basic framework on how investors decide whether to consume their income or forgo some current consumption and invest their money in the capital market. Economists use the framework to describe how people make investment decisions. To briefly answer this question I will first define what is the capital market compared to other markets. Next, I will briefly examine the context of an investment decision within the context of classical utility theory. Finally, I will discuss some of the tools investors use to choose one investment over another.
Financial markets are generally segmented into debt and equity markets or into money and capital markets. The most common way for an individual or firm to obtain money is to borrow money by issuing a debt instrument such as a corporate bond or mortgage. These instruments are in essence an IOU where the borrower enters into a contractual agreement to pay the holder (lender/saver) some dollar amount at regular intervals (interest and principal) over a specified time period. Maturity is the number of years, months, etc. until final payment is made. This market is generally called the debt market and is the most widely used method to raise funds.
The second method for a firm to raise money is by issuing equities such as common stock. Equities are a claim against the firm’s income and assets. If you own one share out of a 100 shares then you have a 1% claim against the company’s income and assets. You make money either through dividend payment where the company shares the income with the shareholders, or by selling the share for a profit base on the market appreciation of the company’s assets and projected income stream.
Another way to distinguish markets is based on the maturity of the securities traded. The money market is a financial market in which only short-term debt instruments are traded which have maturity dates less than one-year. The capital market is the market in where longer-term debt (greater than one-year) and equity instruments are traded. Money market securities are usually more widely traded and tend to be more liquid because of their short maturities. Liquid refers to the ability to sell the instrument on the market quickly to raise cash.
The Money Market comprises:
- Negotiable CDs – A certificate of deposit (CD) that is a debt instrument sold by banks to depositors that pay annual interest of a given amount at maturity pays back principal.
- Commercial paper – is a short-term debt instrument issued by large banks and well-known corporations.
- Repurchase agreements (repos) are effectively short-term loans for which another instrument serves as collateral.
- Federal Funds (FED Funds) are typically overnight loans between banks of their deposits at the Federal Reserve. The fed funds rate the interest paid on fed funds borrowing is a closely watched rate. It is a barometer of how tight is the credit market.
- U.S Treasury Bills are short-term government instruments issued on one, two, three, and six month maturities. US Treasury bills are the most liquid of all money market instruments because they are the most actively traded.
The Capital Market on the other hand generally comprises longer-term investments including:
- Stocks are equity claims on the net assets and income of a corporation. Stocks are divided into common shares and preferred shares.
- Mortgages are loans to households or firms to purchase land buildings etc. The land or buildings serve as collateral to the loan.
- Mortgage backed securities are bond like debt instruments backed by the individual mortgages which are collected together whose principal and interest payments are collectively paid to the bond holder.
- Corporate bonds are long-term bonds issued by corporations with very strong credit ratings. The typical bond pay the holder semi-annual interest payments and pays the face value (principal) at maturity. They may be sold in the secondary market at par their face value, or at loss or gain.
- Municipal Bonds which are debt instruments issued by city and state government.
- Finally long-term Treasury Bonds which are long-term debt instruments issued by the U.S. government.
An individual, or firm, who invests in the capital market are then generally investing in long-term instruments greater than one-year. What motivates an individual or firm to invest in the capital market? In the classical view, economists segment investment into an intertemporal choice between two alternatives: current consumption and future consumption. To describe this relationship economist often use marginal utility analysis or indifference curve analysis.
As in the graph below economists begin with the individual choice to save or invest. The individual will save and consume at level that gives him/her the highest level of satisfaction (utility). This framework is referred to as the Classical Utility Theory of Investment. The highest level of utility is depicted in the graph below by the indifference curves U1 through U4 for a given level of income (budget). The highest attainable level of utility is point C1 where U3 is tangent to the individual’s budget line.
We can apply this same analysis to the owner of a single firm who can either: consume the firm’s present earnings by liquidating the assets (points O,A) in the next graph, or can save / invest into future returns (points A, D). Note the production frontier acts like a budget line in the first graph. In this case the production frontier represents the combinations of savings and consumption that is used to produce wealth / utility. Note the curved shape of the frontier is due to the law of diminishing returns. T he level of consumption and investment also equal to the point of highest utility at point C1.
Introducing the capital market allows us to examine investment decisions where there are many owners (shareholders) – this is called the Separation Theorem. The capital investment decision becomes the company (managers) undertake physical investment until the return from the investment equals the market rate of return/interest at point P in the next graph. This level of investment results in some dividend flow or appreciation of wealth to the shareholders. Shareholders make their financial decision by either borrowing or lending in the capital or money markets until their individual time value of money equals the market return (the line depicted by 1+r where r is the market return below). This results in the highest aggregate utility at point C2 indifference curve U2. In other words, the individual investor will only invest in the capital market if he or she can get a return equal to the average return in the capital market. This is the point where the investor’s utility (e.g. satisfaction) is tangent to the Capital Market Line (CML). More importantly, by forgoing some current consumption and investing in the capital market, the investor can raise his or her utility to a higher level than what could be obtained just by the income of the business (C1 to C2, U1 to U2 in the graph below).
Now if the investment, e.g. a stock purchase, does not achieve the same return as the capital market, the investor will forego that investment and look for other alternatives in the classical view point. Another alternative is to not forgo current consumption at all. In other words one could decide to consume all their income and not invest at all if the market return does not compensate for all the perceived risks associated with the investment including credit risks, inflation risks, etc. These risks arise due to a phenomena call information asymmetry due to imperfect information in the markets. “The borrower always knows better than the lender (investor e.g. saver) their ability to pay back the investment.”
Once an individual decides to invest in the capital market, how do they choose between investment alternatives? There are various tools (equations) that help. These tools generally measure differences in asset (bond) prices and interest. Higher bond prices will affect the supply and demand for bonds. Conversely interest rates will also affect the supply of and demand for money in the economy. Some of the factors that affect financial asset demand (or the demand for bonds) are:
- Wealth: the total resources owned by the individual, including all assets. The more wealth an individual has in the form of cash, the more likely he or she will use some of the wealth in financial assets.
- Expected Return: the return expected over the next period on one asset relative to alternative assets. The higher the expected return on that asset relative to all other alternative investments, the more likely investors will invest in that asset.
- Risk: the degree of uncertainty associated with the return on one asset relative to alternative assets. Since investors tend to be risk-adverse, they will generally choose less risky investment
- Liquidity: the ease and speed with which an asset can be turned into cash relative to alternative assets. The easier it is to turn the asset into needed cash, the more likely investors will invest in that financial asset compared to alternative investment.
One’s wealth, risk and liquidity are all factors that influence expected return. For example, if interest goes up, the relative opportunity cost of holding on to cash as an asset goes up compared to investing in the capital market. A similar relationship applies to holding cash compared to bond prices. The more risky an asset, the higher the expected return to compensate for the additional risk. Of course the less liquid an asset, the greater the chance of interest rate risk, and hence the investor will require a higher expected return.
Expected return, then, is the first tool or measure an investor will use to choose between alternative investments. It is simply what the investor expects to receive when he or she sells the asset at the end of the investor’s horizon or holding period. It is the difference between what the investor paid for the asset verses what the investor receives when he or she sell the asset. The holding period is the time the investor plans on holing on the asset before selling it. The holding period may be less than the stated maturity of the asset. The expected return is calculated by a simple formula:
Expected Return =
Where P2 = the selling price
P1 = the purchase price
Now if the purchase price is $100 and the expected selling price is $110, then the expected return is $10 ÷ $100 or 10%. Note, the expected return is what the investor expects to receive. The realized return, on the other hand, uses the same formula but, measures the actual selling price verses the original purchase price. For example, it is possible interest rates or assets prices may move in an adverse direction resulting in a realized loss, or some return that is less than what the investor originally expected when he or she made their asset selection.
While the expected return and the realized return measures the associated profit one can make on the asset, it does not take into account the “time value of money”. The general principal behind the time value of money is a “dollar today is better than a dollar tomorrow.” The general discounted cash flow formula take into account the time value of money. Why?
A dollar deposited today can earn interest and become $100 x (1+i) one year from today, where “i” represent the annual interest rate. If the annual interest rate =s say 10% than the amount of money one would receive a year from now would be $110 or $100 x (1.10). This is called the Future Value of an investment. We can generalize this relationship in the following formula:
CF*(1+i) where:
CF = cash flow invested
i= the annual interest rate
On the other hand, say you expect to receive $110 one year from now. The net present value formula tells you how much that $110 is worth today or its “present value.” The formula is simply the inverse of the future value formula. Applying the formula to our expected future cash flow we get:
PV = $110 ÷ (1.10) = $100
We can generalize this relationship in the following formula:
The superscript “n” represents the forward period in this case which is one year and hence we can drop it in our original $110 example. However this brings up an important point. If we have a three-year investment and there are multiple cash flows we cannot just simply substitute 3 for “n” in the formula. The reason is that the net present value of each cash flow will be different due to the time value of money. For example, assume we have 10 –year $1,000 bond with a stated coupon of 10% per year. The bond would pay us $100 each year until maturity where we would receive the interest and outstanding principal. We would calculate the Net Present Value (sometimes referred to as Discounted Cash Flow (DCF) as:
Note the present value of the first year’s payment is $90.91 whereas the value of the second year’s payment is $82.64. By the 9th year the present value is only $42.41. This means that the present value of the cash flows in the earlier years, are higher than those in the latter years. It also means you cannot directly compare the $100 dollars earned in the first year to that earned in the next year, etc..
Another interesting facet is if one holds onto the investment to its stated maturity, the present value of the cash flows will equal the face value of the bond, in this case $1,000. This is often referred to as the market-value of the instrument. In other words, the market value of an instrument when held to maturity will always equal its face value. The investment decision then becomes which investment will give the highest NPV for the same maturity or holding period. Here interest is the major factor because you want to accumulate some level of income over the investment horizon.
Now suppose you want to sell the bond before it matures. That is your holding period is less than the stated maturity of the bond. If interest rates change then the market value of the bond may also change. For example, suppose the current interest rate move to 11%. If you needed to get your money before maturity and were to sell the bond in the market, you would have to sell it for a loss of $58.89 base on the net present value of its cash flows assuming a higher discount rate as in the example below. You would use the higher discount rate to value the bond because buyers could obtain that rate in the market and you are selling them an instrument that pays a lower rate. The only way to incent them to buy your bond is to sell it at a loss (discount) to compensate for the lost future income from the 1% interest rate difference.
When interest rates decline the investor faces a similar situation. In this case the buyer would have to pay the investor (seller) a premium to offset the lost future interest income. Without the premium the original investor would have no incentive to sell the bond because the alternative is to take the money and invest it into lower interest rate instruments.
Focusing on maturity ignore the fact that some cash benefits are received before maturity (can be reinvested) and the benefits may be substantial. Another tool that investors utilize is Duration. Duration is the weighted average time over which he cash flows form an investment are expected, where the weights are the relative present values of the cash flows. Consequently it is a time measure not an income measure. The table below shows how it is calculated.
Each time period is weighted by the cash flows present value contribution to the overall net present value. For instance, the first period’s PV represents 9.1% of the total PV of $1,000 ($90.91÷$1000). The 9.1% is then multiplied to arrive at 0.09 element of a year. The sum of the weighted time elements gives the duration of the instrument. In the above example the duration for this bond is 6.76 years.
Higher yields lead to lower durations. As the yield increases the present value of the distant cash flows gets exponentially smaller thus the weight given to distant time periods in the numerator get smaller lowering the duration. Moreover, duration of any instrument is positively related to maturity, except for maturities in excess of 50 years. Why is this important? The answer: for a given change in market interest rate, the percentage change in an asset’s price (PV) and are proportional to the asset’s duration. Hence longer duration instruments are subject to greater price changes (exhibit greater price elasticity). This is expressed by the following formula:
-Duration × [Di ÷(1+i)]
Shorter duration instruments then are less sensitive to interest rates and are generally preferable to longer duration instruments. The investment decision then encompasses the investor’s:
- Holding Period
- Expected Return
- Present Value of the Cash Flows
- Instrument’s duration and sensitivity to interest rate changes.
Again, if the investor decides to hold the bond to maturity- then the investment decision is only dependent on expected return and the holder’s investment horizon as the NPV of the instrument will equal its current market value or face value.
Other factors that come into play in the investor’s decision and utility maximization include liquidity – how easily the instrument can be converted into cash if needed. This is driven by supply and demand in the market. Most often investors prefer more liquid instruments. The other factor is credit risk – the likelihood the borrower will not pay back the bond (loan). Higher perceived credit risk requires the borrower (bond issuer) to pay a higher interest rate to compensate for the additional risk.
In summary the capital market is an important mechanism to transfer funds between borrowers and investors. Investors will choose between current and future consumption at a level that maximizes their utility or satisfaction. By lending and borrowing in the capital market individuals can move to a higher level of utility then what they could have achieved without capital markets. The investor’s expected return and whether it can be achieved in the capital market is the driving factor for investment. In addition to expected return, investors also take into account other factors like their holding period, the net present value of the cash flows, the duration and interest sensitivity of the instrument, and its credit and liquidity risks.