There are two methods by which these funds may be transfered. One method is through financial intermediation which involves the use of a comercial banking system to attract deposits from individuals and institutions and make loans to other individuals or institutions. 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.

A share of stock conveys certain ownership rights to the holder such that person may share in the profits or earnings of a publically-held corporation and, in some cases, have voice in how that company is managed. A bond is a 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 meed budgetary needs.

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 commerical 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 liquitity. A final option available to the household would be to remain perfectly liquid, that is, to financial risk and hold these surplus funds as cash (money) eventhough 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.

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: 

P_bond =
PV_bond = S R_t(1+r)^-t + F(1+r)^-30 or (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 (so that F = R/r) then as 'N' approaches infinity, the expression reduces to: 

P_bond = (R/r)

which is known as the present value of a perpetuityand provides a simple formula for understanding the relationship between asset prices and asset yields (or interest rates).

Bonds are first issued in primary bond markets where the seller represents the borrower and the buyer represents the lender. 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 their 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. 

In order to maintain liquidity with respect to bond ownership, a secondary bond market also exists for the buying and selling of these bonds at current interest rates. This buying and selling does not represent any new debt activity but rather the exchange of bonds among investors. 

When interest rates fall, new investors may have the option of buying new bonds in the primary bond market at the new (current) interest rates and recieving lower coupon 'R' payments or existing bonds in the secondary market with perhaps higher coupon payments. In order to maintain competition with respect to yields between new and existing bonds, investors will often offer a higher price for existing bonds.

Treasury Bills and other Short-term Debt instruments.
Most Treasury bills and/or commercial paper (due to their short maturity -- 1 year or less) are discounted at the time of sale rather than pay some coupon payment over the holding period. This discount is calculated as follows:

Discount  = (F)(r)(d)
                 365

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 about $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)(0.10)(182) = $49,683
365

$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 = 5.23% semi-annually
$950,137

(1.0523)² - 1 = 10.7% annually

Common Stock.
Common stock represent ownership (equity) shares in publically-held corporations. These rights of ownership often include a share in the profits (earnings) of that corporation. However, these earnings may be used either as a source of internal financing , known as retained earnings, or paid out to the owners as dividends. The value of the corporation is based on these earnings whether they are paid out or not. 

Much is made of the price/earnings (PE) ratio of different common stocks with a low PE being often prefered to a high PE for a given stock. This ratio is often used as a benchmark to determine if that corporation is over-valued (too high) or under-valued (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:

                    P_asset = (R/r)    or     Yield_asset = R/P_{asset or}

Yield_stock =  Earnings/P_share

The earnings-over-price ratio is often in precentage 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: 

 r = D/Pshare + E[g]

where 'r' is the rate of return, 'D' is the annual 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: 

r = ($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 based on similar investments.  Solving for 'P', we have: 

P_share = D/(r-g)

or given an annual dividend 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      = $40.00
(0.08 - 0.03)

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. 

The Expected Total Rate of Return (ETRR)
Since both stocks and bonds are marketable securities, the potential exists for changes in market price which may translate into capital gains or perhaps capital losses. A capital gain occurs when the selling price of a security 'P_s' exceeds the purchase price 'P_p'. If the selling price is less than the purchase price then the owner will incur a capital loss. 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 rate of return 'ERR' defined as follows:

ETRR = r_n + (E[P_s]- P_p)/P_p

where 'r_n' represents the normal rate of return (current yield) on the security and 'E[P_s]' represents the expected selling price of the security at some point in the future.

Expectations about the selling price (E[P_s]) 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 or perhaps be negative if with a significant decline in the selling price.

If the ETRR is negative, then it is better for the investor to hold his/her wealth in the form of cash balances where the ETRR_cash is equal to zero. Stated differently, if interest rates are expected to rise significantly, wealth-holders will make cash a larger part of their portfolios.

• Bond
• Capital Gain
• Capital Loss
• Coupon (R)
• Direct Finance
• Discount (sell at a)
• Expected Total Rate of Return (ETRR)
• Face Value (F)
• Financial Intermediaries
• Financial Markets
• Par Value
• Premium (sell at a)
• Present Value
• Present Value of a Perpetuity
• Price/Earnings (PE) Ratio
• Primary Markets
• Secondary Markets
• Share of Stock