Valuation of Securities

Valuation

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Contents:

• Present Value

• Net Present Value

• Asymetric Information

• Productive Investment

• Riskless Securities

• The Law of One Price

• Financing Methods

• The Principle of Value Additivity

• Risky Debt

• Re-allocating Value Among Groups of Claimants

• Inferring Atomic Security Prices

• Financial Engineering

• Opportunity Sets

• Consumption and Investment Decisions

Present Value

How much is an apple tree "worth" in our economy? Such a question is best interpreted as "how many present units of the numeraire should be traded for the apple tree?". The answer is found by calculating the cost of obtaining the same set of payoffs in another way. The result is the present value of the apple tree. The process of determining the present value of a security or productive investment is termed valuation.

In principle, the process is very simple. Recall that the tree will provide 63 apples if the weather is good and 48 if it is bad. Dealer G will provide the former for 0.285*63=17.955 present apples. Dealer B will provide the latter for 0.665*48=31.920 present apples. The total cost of obtaining the same results in this other manner will thus be 17.955+31.920=49.875 present apples. This is the present value of the apple tree, as shown in the figure below.

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There is nothing metaphysical about this concept of value. It is based entirely on the cost of obtaining a fully equivalent set of payments. If an apple tree is selling for less than this, one can obtain an arbitrage by buying the tree and selling its production through the dealers. If a tree is selling for more, one can offer the same outputs, sell them and use the proceeds to buy securities from the dealers to guarantee delivery. In each case, there will be something left over for the arbitrageur.

In real markets, such opportunities are few and fleeting. In an arbitrage-free market, they are totally absent --...