Linkages between value based performance measurements and risk return trade off: theory and evidence/Vinculos entre las mediciones de valor basado en el desempeno y el dilema Riesgo Retorno: teoria y evidencia.
| Autor | Celik, Saban |
INTRODUCTION
The primary objective of this paper is to examine one of the core concepts of finance, asset pricing, for the purpose of explaining asset dynamics which have been extensively analyzed by economists, statistician, econometrician, mathematician and financial scholars. More interestingly asset pricing becomes a starting and also pioneering area for many groundbreaking models and extents new perspectives in several fields. In the simplified term, asset pricing can be defined as a common field of economics, finance, mathematics, statistics, econometrics and even psychology. In order to emphasize why study asset pricing, Cochrane (2005) underlined that:
Asset pricing theory tries to understand the prices or values of claims to uncertain payments. A low price implies a high rate of return, so one can also think of the theory as explaining why some assets pay higher average returns than others. To value an asset, we have to account for the delay and for the risk of its payments. The effects of time are not too difficult to work out. However, corrections for risk are much more important determinants of many assets' values. For example, over the last 50 years U.S. stocks have given a real return of about 9% on average. Of this, only about 1% is due to interest rates; the remaining 8% is a premium (1) earned for holding risk. Uncertainty or corrections for risk make asset pricing interesting and challenging (xiii). The challenging point as Cochrane underlined is coming from how to adjust the risk under uncertainty. The way we approach the problem is a rather naive way of thinking which can be seen as a common way of financial economists as follows (2): We would like to start with the following question: Is price (3)of an asset equal to its value (4)?
price = value
Such a simple question can be easily answered as "No". However, this seemingly simple question can lead us thinking of under which conditions such equality will be held. It is often heard that "this car is sold below its value" or "the firm asset is lower than its market price". It seems that the price and the value are two different concepts. On the one hand, there is an indicator that is price and on the other hand, there is a notion, value, which is quantified through a price. However, the main difference is the factors that affect price and value. This paper is the first attempt to examine the linkages between risk-return trade off based on value based performance measurements. The second section shows theoretical roots of asset value and pricing process. In the third section, we review the literature devoted to value based performance measurements and in section four we offer empirical analyzes of the linkages between value based performance measurements and risk-return trade off.
THEORETICAL LINKAGES BETWEEN VALUATION AND PRICING
Figure 1 describes the price-value relationship whereas it is far away from being realistic representations. The main purpose is to draw a general framework to show how equilibrium exists under the factors that affect price-value equilibrium (5) level. The main factor that affects the price of an asset is its demand in market. If there is no demand for a particular asset, it does not make any sense to price it. It is implicitly assumed that such asset can be marketable. On the other spectrum, the main factor that affects the value of the asset is its supply side. A car producing firm does not sell all of its products on the same price. "Why?" Since the qualifications of cars are different, their prices are quoted on different levels.
In a formal demonstration, we define the following properties:
V (t) = (SUPPLY + [e.sub.s]) (1) P(V (t)) = (DEMAND + [e.sub.D]) (2)
where V(t) is value function with respect to time (t), SUPPLY is the main factor (but only) affecting the value creation process; [e.sub.s] is undefined factor affecting the process; P(V(t)) is price function with respect to value function V(t); DEMAND is the main factor (but only) affecting the price; [e.sub.D] is undefined factor affecting the process.
Proposition 1: the value of the asset is constant at certain time, t.
Proof 1: if we stop time, the value of any asset, including human value, will be fixed. As human beings, we would not turn older since time has been stopped.
Proposition 2: if we hold the demand constant between the two periods, the price of the asset will not be changed unless the value of the asset is changed.
Proof 2: What makes the value of any asset different in the public is its desirability, its demand. We implicitly assumed that the covariance between supply and demand is zero. However, it is true that supply and demand affect each other. The critical justification here that saved and proved our proposition is to isolate the impact of demand on supply and therefore on value, as depicted in Figure 1.
It is not intended to say that the demand and the supply do not affect each other and price-value equilibrium. This is a general framework in the sense that the price-value equilibrium is nothing more than a theoretical discussion. However, the definitions we used for value and price play important role behind the above discussion. We emphasize the role of value and assume that there exists a value before demand which determines its price level. The critical task is to establish its real (actual) value (equivalently economists used the term fair value and accountants used the term intrinsic value). The present paper does not claim that there are no other factors affecting the value and price or equivalently supply and demand for a given asset.
For this reason, we define [e.sub.s] and [e.sub.D] as an undefined component of our theoretical discussion. The unique part of this view is that we do not follow utility based equilibrium as it is classical in determining prices in economics. We emphasize a more compact form and derive the theoretical linkages between value and price. In a discrete time setting, we showed how equilibrium existed in Figure 1. It is necessary to describe what kind of process there should be for price and value in continuous time (intertemporal settings).
In Figures 2a and 2b, a representative value process is depicted. As it is seen, this representativeness looks like a product life cycle (or equivalently life cycle of the firm). It can not be extended for all products because some products such as consol, a financial product paying fixed cash payments developed and maintained by Bank of England Consols, simply have no maturity. However, in Figures 2a and 2b there is an ending time, T (e), for the product. The important inference derived from them is that at equilibrium, the (ending) price and the (real) value for the asset is the same. In other words, at time t (1), the value of the asset is a vertical line implying that there is a constant value for the asset. The level of its price is determined by its demand at time t (1) and the corresponding point represents the equilibrium price-value point. However, it is simply assumed that the demand for the asset depending upon the value of the asset may change, so that the level of the price increases or decreases. At the ending period, since there is no value for the asset at all, it should not be expected to be priced, as indicated by an empty circle in Figures 2 a and 2b. The most difficult part in the described framework is how to define the exact price and value process for different assets, such as financial assets or nonfinancial assets or even for human capital.
Economists usually make specified assumptions to clarify the situation in which their predictions will be held. Let us start with a general case to emphasize how a value of an asset can be determined in one period model.
Assumption 1: There is only one period but two dates where transaction takes place.
Assumption 2: There is zero interest rate.
Assumption 3: There is zero inflation.
Assumption 4: There is zero risk.
Assumption 5: The rest of the factors that may affect the transaction remains constant at two dates (ceteris paribus). This assumption is required for the existence of price-value equilibrium. As it is noted earlier, if we hold the demand constant between the two periods, the price of the asset will not be changed unless the value of the asset is changed.
Figures 3 to 7 show how a value of an asset can be changed under these assumptions and in lack of assumptions 2, 3 and 4 mentioned above.
Under the assumptions 1 to 5, it is clear that we are certainly dealing with a sure value due to the fact that we fixed every factor that may affect the value of an asset in one way or another in the next period. This is the starting point to illustrate from certain to uncertain value. Despite the fact that valuation under uncertainty is the main theme of asset pricing, in this section we will just present it in a simplified manner.
Relaxing assumption 2: There is a constant interest rate that can be earned in the market (later we will define this rate as risk free).
Introducing a constant interest rate leads us to discount the next period value to the present. As it is well documented in financial text books, present value calculation is usually used to evaluate the required rate of project. How this rate is to be determined is the subject of the models that are explained in the following sections.
Relaxing assumption 2 and 3: There is a constant interest rate denoted as [r.sub.c] that can be earned in the market and an inflation rate, denoted as i (inflation is usually assumed that it is adjusted in risk free rate or in risk premium whereas it is necessary to demonstrate how it takes place in valuation).
The value of a Turkish Lira today is not equal to the value of a Turkish Lira tomorrow if there is an inflation and equivalently opportunity cost. The impact of inflation results on nominal returns and we usually deduct the impact and gain the real return. Therefore, the inflation rate...
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