and the Yield on Different Financial Instruments
In an aggregate economy, we often find that the expenditure needs of one sector (households) is less than income or revenue resulting is a surplus of funds. These funds are known as savings, and more specifically, private savings. The opposite is often true for the business sector and government sector of the economy. For these sectors expenditure often exceeds revenue such that there is a need to borrow funds from the household sector. The transfer of funds from one sector to another in the form of lending and borrowing is facilitated by financial markets and different financial instruments.
There are two methods by which these funds may be transferred. One method is through financial intermediation which involves the use of a commercial banks and banking system to attract deposits from individuals and institutions and make loans to other individuals or institutions. The key assets for these banks are money (cash balances) and reserves. These banks act as intermediaries between lender and borrower hopefully minimizing the transactions costs (risk-assessment of borrower and liquidity needs of the depositor) related to this type of financial activity. A second method is known as direct finance when borrower and lender directly interact through activity in equity or debt markets. In this case the lender will buy financial instruments (shares of stock or bonds) being sold by borrowers.
Households with surplus funds (income in excess of spending needs) will seek to choose the best way in which to use these funds. This best way depends on the liquidity needs of the household, attitudes towards financial risk, and desired return when these funds are made available to financial markets. These households may deposit these funds in a commercial bank or savings institution, maintain a high level of liquidity (easy and quick access to these funds), be exposed to small risk of capital loss, and earn a small return in the form of simple interest. An alternative would be to buy a share of stock or a bond where the returns may be higher in the form of dividends, interest, and capital gains. However, this activity exposes the individual to more risk (default in the case of bonds and capital losses) and less liquidity (having to convert these types of financial instruments into cash). Other possibilities would be to buy commodity assets or properties that often pay no interest or dividends but may appreciate over time. The returns may be greater combined with more risk and less liquidity. A final option available to the household would be to remain perfectly liquid, that is, to avoid financial risk and hold these surplus funds as cash (money) even though this type of asset pays no return (interest, rents, dividends, or capital gains).
The information made available by financial markets (as well as commodity and property markets) to the owners of these surplus funds helps in making decisions about the best use of these funds. However, because perfect liquidity is an option, money plays a special role in financial market activity.
Financial Markets may be divided up into two related markets. One set of markets are primary markets where the seller of a financial instrument represents the borrower and the buyer of that instrument represents the lender. It is in these primary markets where all new borrowing and lending take place via direct finance. Invesement Banks play a special role in primary market activity in that they are the institutions that handle the underwriting (issuance) of new bonds or new shares of stock to the marketplace.
In order to maintain liquidity with respect to ownership of these financial assets, secondary markets also exists for the buying and selling of these instruments. This buying and selling does not represent any new debt activity but rather the exchange of stocks, bonds and other securities among investors. This buying and selling activity governs the price of these instruments and, as discussed below, their compeitive yields or rates of return.
Two common financial instruments, traded in capital markets are Stocks (or Equities) and Bonds. A share of stock conveys certain ownership rights to the holder such that this person may share in the profits or earnings of a publicly-held corporation and, in some cases, have voice in how that company is managed. A bond is a medium or long term debt contract explicitly stating the amount borrowed and to be repaid, date of repayment, and interest to be paid by the borrower to the lender. Bonds may be issued (sold) by large corporations, municipal governments, or the federal government to meet budgetary needs.
A third type of financial asset also exists in the form of money market instruments which represent short term debt instruments.Bonds and Inverse Relationship between Asset Prices and Asset Yields
A Bond represent a long-term debt contract between a borrower and lender. The terms of this contract include the face value (the amount borrowed per bond issued) F, a rate of (annual or semi-annual) interest r, and the maturity (the date when the face amount must be repaid) N. The coupon of the bond R represents the periodic dollar amount of interest paid to the lender/owner of the bond over the life of that bond. This coupon amount is calculated simply by taking the product of the face value and rate of interest:
R = (F)(r)
The price (or present value) of a 30 year bond that pays an annual coupon of 'R' and has a face value of 'F' at the end of 30 years is defined by the following formula:
Pbond = PVbond = Σ[t=1,30] Rt(1+r)-t + F(1+r)-30or using the formula for the sum of a geometric series:
= (R/r)[1 - (1+r)-30] + F(1+r)-30
If the rate of discount 'r' is the same
as the printed interest rate on the bond
Pbond = FAs 'N' approaches infinity, (the Bond never matures) for any rate of discount, this expression reduces to:
Pbond = (R/r)
which is known as the present value of a perpetuity and provides a simple formula for understanding the relationship between asset prices 'P' and asset yields 'Ψ' (or interest rates).
Ψ = R / Pbonds
The coupon payment and face value are fixed by contract over the life of the bond. If market interest rates are the same as the printed rate of interest on the bond, then the price (present value) of that bond is the same as its face value-- the bond sells at par-value. If market interest rates have risen, prior to the sale of the bond, such that investors can receive higher yields on competing investments; then, the market price of the bond will be less than its face value. The bond will sell at a discount. If the opposite is true such that market rates have fallen, then the bond will sell at a premium -- the market price will exceed its face value. Bond prices move in the opposite direction of market interest rates.
Activity in secondary markets often reflects changes in the economic environment where buying and selling activity is driven by changes in inflationary expectations, changing attitudes towards (credit and interest rate) risk, and changes in perceived uncertainty about the future.
For example, suppose that information becomes available such that investors revise their inflationary expectations upward. Given that inflation lowers the real rate of return received by lenders (or those holding bonds and other securities), these individuals will begin to sell existing bonds in the secondary market. This selling creates a surplus of bonds being offered such that bond prices must fall to induce potential buyers to accept these securities in an accelerating inflationary environment. With this decline in bond prices, secondary bond yields increase:
R / Pbonds = Ψ
When yields rise, investors have the option of buying existing bonds in the secondary bond market or new bonds in the primary market. In order for these new bonds to be competitive with existing bonds, a higher rate of interest must be offered. This higher rate of (nominal) interest will reflect the upward revision of expected inflation.
Secondary markets also facilitate portfolio adjustments in reaction to a changing economic environment. For example given two different assets one being higher risk (a BBB rated 5 year corporate bond) and the other no risk (i.e., a Treasury Note), we would expect that:
ΨCorporate-BBB > ΨT-Note such that ρ = (ΨCorp.-BBB - ΨT-Note)
If for some reason the perceived risk of holding debt instruments were to increase, we would expect to observe a flight to quality – a selling the corporate bonds and buying of Treasury instruments.
PCorporate-BBB, ΨCorporate-BBB and PT-note, ΨT-noteThis increase in perceived risk will translate into higher risk premiums in secondary markets and thus require that riskier borrowers pay a higher premium (higher nominal interest rates) in primary markets.
Pshare = ΣEt(1 + r)t
Much is made of the price/earnings (PE) ratio of different common stocks with a low PE being often preferred to a high PE for a given stock. This ratio is often used as a benchmark to determine if that corporation is overvalued (too high) or undervalued(too low) by the stock market based on its current trading price. This ratio is nothing more than the reciprocal of a simple yield calculation based on the present-value of a perpetuity formula:
Passet = (R/r)or
Ψasset = R/Passetor
Ψstock = Earnings/Pshare
The earnings-over-price ratio is often in percentage form and by taking the reciprocal we define an integer expression that is often easier for use in making comparisons among different stocks. However, for purposes of evaluation, we can use the reciprocal of the PE and compare with investments of equivalent risk and maturity or against the yields on perhaps safer marketable assets.
What is unique about equity instruments is that their value often is based not just on the periodic return (earnings in this case) but also the expected rate of growth for the corresponding corporation. The rate of return on common stock is often (usually for well-established mature corporations) calculated by the following formula:
Ψ = E/Pshare + E[g]where 'Ψ' is the rate of return, 'E' represents annual earnings (or dividend), 'P' is the purchase price of a share of the stock, and E[g] is the expected growth rate in future dividends.
Given an annual dividend of $1.00, a purchase price of $30.00 per share, and an expected growth rate of 5%; the rate of return would be:
Ψ = ($1.00/$30.00) + .05 = .0333 + .05 = 8.33%
This formula can also be used to determine the appropriate price to be paid per share of stock given expected growth rates in the annual dividend and some measure of the rate of return 'r*' based on similar investments. Solving for 'P', we have:
Pshare = E/(r* - g)
or given annual earnings of per share of $2.00, an expected (or required) rate of return of 8%, and an expected growth rate in future dividends for that company of 3% per year; we have the calculate purchase price of:
P = $2.00 / (0.08 -0.03) = $40.00
Quite often the explanation for the existence of both buyers and sellers of the same shares of stock is that buyers expect higher growth rates in future dividends relative to the expectations of sellers.
Treasury Bills and Money Market
Discount = (F)(r)(d)
where F is the face value (the amount borrowed or principal), 'd' is the days to maturity, and r is the market interest rate.
For example, if a business needs to borrow roughly $1,000,000 for six months (182 days) to finance seasonal inventory needs, and current market rates are 10% then the amount of the discount would be:
$1,000,000 - $49,683 = $950,137
However the full $1,000,000 is repaid at the maturity date.
The rate of return (the yield) on this short-term debt instrument is equal to the amount of the discount divided by the amount borrowed or:
$49,683 = Ψ = 5.23% semiannuallyor an effective rate of:
(1.0523)2 - 1 = 10.7% annually
Trading of money market instruments of particular face value ‘F’ is based on prices offered for these instruments in secondary markets or via auction in primary markets. The yield is then computed as follows:
Ψdiscount = (F - Poffered)/Poffered = (F - Poffered) - 1such that as,
Poffered , Ψdiscount
The Expected Total Rate of Return (ETRR)
Capital gains and losses can either enhance or reduce the normal rate of return on a given security. For this reason, acquisition of these securities are often based on expectations of future capital gains in addition to the normal rate of return. This overall yield or expected total rate of return 'E[TRR]' defined as follows:
E[TRR] = rn + (E[Ps]- Pp)/Ppwhere 'rn' represents the normal rate of return (current yield -- R / Pp) on the security and 'E[Ps]' represents the expected selling price of the security at some point in the future.
Expectations about the selling price (E[Ps]) depend on expected changes in market interest rates (such that these prices and interest rates will move in opposite directions), and/or expected rates of growth in earnings (in the case of equities). Lower market interest rates or higher rates of growth can lead to capital gains on the sale of these assets such that the ETRR is greater than the current yield. If market interest rates are expected to increase or growth rates in earnings are revised downwards, then these asset may sell a price below the price paid and thus a capital loss results. In this case the ETRR may be less than the current yield and, in the case of an extreme increase in interest rates, be negative if with a significant decline in the selling price (the capital loss more than offsets the normal yield). In situations where investors expect the total rate of return to be negative on a financial asset, cash will present a suitable alternative given that:
TRRcash = 0
Thus solid reasons may exist for holding cash in a portfolio of financial assets even though cash does not pay any type of periodic return. In the expectation of capital losses on marketable securities, principal may be preserved by holding cash.
Concepts for Review: