BILL ADONGO

ADONGO'S LINEAR MODEL OF CAPITAL-ASSET

Introduction:

The availability of Central Point Theory open the way for the Central Prediction Theory as long as applied statistics is concerned. The earliest form of more accurate Credibility Theory (or Model) is the Buhlmann and Bultmann-Straub Theory (or Model) which I revolutionized as Central Credibility Theory. The availability of the Central Credibility Theory (or Model) in turn open way for the establishment my Central Rating Theory(or Model) that can applied practical in most Insurance and Financial Industries.

The Central Point Theory is not only the  cause of my Theories Mention above but also applied by me to produce practical theories(or Models)  like Central Cost and Pricing Model, Inventory Theory(or Model) of Uncertainty, Strategic option Model, Minimum Uncertainty Theory(or Method), Growth Rate, Growth Theory, Billian Capital Stock  Valuation Theory(or Model), Base Rate Model and Billian Interaction Theory(or Model).

I cannot talk of Point Values Interval Law without Central Point Theory. One of the useful areas in which I can apply my Point Values Interval Law is assessment of Systematic Risk and Beta Coefficients.

                                                                 

PROBLEM OF STATEMENT

Existing Theory in this field of analysis is limited because; people could not apply the existing concept to perfectly predict infinite expected returns of portfolio in order differences or infinite betas of portfolio in order of differences that proved important here. It could not predict some infinite different possible portfolio expected returns and betas by varying the percentages invested in two assets. The existing Theory on assessment of systematic risk and beta could not also use to perfectly predict corresponding relationship between expected returns and betas in order of differences to infinity.

SOLUTION TO THE PROBLEM

This theory of mine is to perfectly predict infinite expected returns of portfolio in order differences or infinite betas of portfolio in order of differences. This theory is also possible for predicting some infinite different possible portfolio expected returns and betas by varying the percentages invested in two assets. My theory also perfectly predicts corresponding relationship between expected returns and betas in order of differences to infinity.

ASSESSMENT OF SYSTEMATIC RISK AND BETA

There is no type of risk that affects a large number of assets than systematic risk. A systematic risk that affects a large number of assets is also known as market risk. The systematic risk principles states that the mean expected return of securities asset are in linear relation and the reward for bearing risk depends only on the systematic risk of an investment in order of differences, the underlying rationale for this principle straightforward: Since unsystematic risk can be eliminated at virtually no linear relation and reward for bearing it. Put another way, the market does not reward risk that are borne unnecessarily.

MEASUREMENT

Since systematic risk is crucial determinant of an asset’s expected return, in their order of differences, we need some way of measuring the level of systematic risk for different investments. The specific measure we will use is called Point Values Interval Law of betas coefficient I have propounded. Beta coefficient is amount of systematic risk present in a particular risky asset relation to an average risky asset. The most important thing to remember is that the expected return in order of differences respectively, on an asset depends only on its systematic risk in order differences. Since assets with betas have expected returns in order of differences. Let us considered security A and security B which expected return, and beta coefficient of portfolio are giving

E(R_P)= {2W_AE[E(R_A)]+2W_BE[E(R_B)]}/2

β_P= {2W_AE(β_A) + 2W_BE(β_B)}/2

The mean amount of systematic risk present in security A asset and security B asset relative to an average security A asset and security B asset respectively are:

E(β_A) =2W_AE(β_A)

E(β_B) = 2W_BE(β_B)

And the mean expected return on asset and security A and B are:

E[E(R_P)] = 2W_AE(R_A)

E[E(R_P)] = 2W_BE(R_B)

POINT VALUES INTERVAL LAWS

LAW ONE:

The mean expected return of security A asset and mean expected return of security B asset are in linear relation. This is simply telling us that, at any mean return of security A asset which are linear related to mean return of security B asset in order of correspondence; the mean return of security A asset is adding itself to infinity when the mean return of security B asset is subtracting itself to infinity and vice-versa.

LAW TWO:

Mean amount of systematic risk present in security A asset and security B asset relative to an average security A asset and security B asset respectively are in linear relation. This is telling us that at any mean amount of systematic risk present in security A asset and security B asset relative to an average security A asset and security B asset is adding itself to infinity when the mean amount of systematic risk present in security A asset and security B asset relative to an average security A asset and security B asset is subtracting itself to infinity and vice-versa.

Suppose we had the following investments.

SECURITY	AMOUNT INVESTED	EXPECTED RETURN	BETA
STOCK A	$1000	8%	0.80
STOCK B	$2000	12%	0.95

What is the expected return on this portfolio? What is the beta of this Portfolio? Does this portfolio have more or less systematic risk than an average asset in order of differences?

SOLUTION

To answer, we first have to calculate the portfolio weights. Notice that the total amount is $3000; of this W_A=1000/3000=0.333333 is invested in stock A. similar W_B=2000/3000=0.666667 is invested in stock B.

E(R_P)= [2x0.333333x8% +2x0.66667x12%]/2=10.666668%

β_p = [2x0.333333x0.080 +2x0.666667x0.95]/2=0.90

The expected beta of asset A is:

E(β_P) = 2W_AE(β_A) = 0.533333

The expected beta of asset B is:

E(β_P) = 2W_BE(β_B) = 1.266667

Applying the point values interval law, we have

E(β_P) = 2W_A)E(β_A)= 0.53, 1.06, 1.6, 2.13

E(β_P) = 2W_BE(β_B) = 1.27, 0.00, -1.27, -2.53

The beta of portfolio in order of differences is:

E(β_P) = (2W_BE(β_B) + 2W_AE(β_A))/2

          =( 1.27+0.53)/2, (1.06+0.00)/2, (1.6-1.27)/2, (2.13-2.53)/2

This portfolio has an expected return 10.67 percent and a betas of ( 1.27+0.53)/2, (1.06+0.00)/2, (1.6-1.27)/2, (2.13-2.53)/2 that is less than 1.00, less than 1.00, less than 1.00, less than 1.00, meaning that this portfolio has less risk in order of differences.

REWARD OF MARKET LINE

Let us now tune our minds to see how risk is rewarded in the marketplace. To begin, suppose that asset has an expected return and beta of portfolio, the risk-free rate is R_f. The risk-free asset, by definition, has no systematic risk (or unsystematic risk), so risk-free asset has a beta of o. The reward market slope of security asset is;

Slop=-R_f/2β_i

        
THE RESULT

The situation have described for asset A and B cannot persist in a well-organized, active market, because investors would be attract to asset A and away from asset B. As a result, asset A’s price would fall. Since price and returns move in opposite directions. The result is that A’s expected return would decline and B’s would rise.

This buying and selling would continue until the two assets plotted on exactly the same line.

REWARD MODEL(RM)

To finish up, if we let E(R_i) and β_i stand for the expected return and beta, respectively on any asset in the market, then we know that it must plot on Reward Line(RL). As a result, we know that its reward-to-risk ratio is the same as the overall markets;

-R_f/2β_i=E(R_m)-R_f

E(R_i)= R_f/2

CONCLUSION 
 Existing Theory in this field of analysis is limited because; people could not apply the existing concept to perfectly predict infinite expected returns of portfolio in order differences or infinite betas of portfolio in order of differences that proved important here. It could not predict some infinite different possible portfolio expected returns and betas by varying the percentages invested in two assets. The existing Theory on assessment of systematic risk and beta cannot also use to perfectly predict corresponding relationship between expected returns and betas in order of differences to infinity.

 This theory of mine is to perfectly predict infinite expected returns of portfolio in order differences or infinite betas of portfolio in order of differences. This theory is also possible for predicting some infinite different possible portfolio expected returns and betas by varying the percentages invested in two assets in order of their differences. My theory also perfectly predicts corresponding relationship between expected returns and betas in order of differences to infinity.