The Riskless Asset Rate Algorithm Finance Essay

It is known that the analysts use the treasury bills, notes or bonds rates, to define the riskless asset and its rate of return for modeling the capital market by the Capital Asset Pricing Model (CAPM), portfolio selection and performance analysis, using the Modern Portfolio Theory (MPT). Due to the fact that these securities do not have a continuous market in Romania and it cannot be followed day by day the evolution of their interest rate, I considered as a possible measure for the riskless security rate (a "pure" interest rate as Sharpe named it) - the free risk interest of the Romanian financial market [William Sharpe (1970)]. By definition, the free risk asset is a financial security, consequently for a more accurate measure, I believe that the representative market for the financial market is the inter-banking market. I defined several financial securities with equal rate of interest with BUBOR, for the borrowing free risk rate, and BUBID for the lending free risk rate, respectively the Romanian inter-banking market rates for lending or borrowing on a period starting with a day to a year. The daily values of these gathered interests in the Analyze Period (AP) (02.07.2001 -08.07.2003 respectively 2 years, each of 245 transaction days) determined the daily average value and the risk associated with every financial security, measured through variance of return. The free risk security rate of return for lending and respectively borrowing is situated in the risk-return space, on the vertical axe, in the points where the capital market line (CML) represented by two regression lines using the daily average rates of BUBOR and BUBID interests, intersects it. In order to point out the fact that the values are valid on the market, in this paper I compared, in the risk-return coordinates, free risk securities thus determined, with currency securities EURO and DOLAR, and also with BET-C synthetic capital asset. I applied in several studies this method for calculating the free risk rate determined in the Romanian inter-banking market and all the results where accurate, providing dates confirmed by the subsequent market trend.

. The riskless asset rate algorithm

In order to measure the rikless security interest rate, or the "pure" interest, I will use the daily dates collected from the Romanian inter-banking market in the AP period and I will define financial synthetic assets, which will be the benchmark within the algorithm. To make the comparison of these rates with the similar rates on the secondary capital market, I will rely on capital market specifically analyze tools, expected return measured by the average rate of return and the risk measured by the variance or by the standard deviation of return. The financial securities which I will define will have the equal rate of return with the BUBID and BUBOR interest rates. The riskless financial security rate was determined throughout financial securities with equal return with the following rates: BUBOR TN, BUBOR 1W, BUBOR 1M, BUBOR 3M, BUBOR 6M, BUBOR 9M, BUBOR 12M and respectively BUBID TN, BUBID1W, BUBID 1M, BUBID 3M, BUBID 6M, BUBID 9M, BUBID 12M. In other words, I used the Romanian inter-banking market rates for lending or borrowing on a period starting with a day to a year. These rates will represent the benchmark for the rikless rate. At the same time, we consider that the market provides a continuous possibility to lend and borrow, and BUBID ON and BUBOR ON are the representatives' rates in the market. The inter-banking market is the representative market for the entire monetary market and includes the risk less security. In the same time, Sharpe defines the riskless asset as a financial security. The investors which will hold positive amounts will lend. Others will hold negative amounts; they will borrow. The total value of riskless securities issued by the borrowers will equal the total value purchased by the lenders. For the daily rates calculation BUBORt or BUBIDt, in the analyze period (AP) accordingly with the stock exchange transaction days, I used the following formula: _Ec. 1A¢â‚¬‘1 where: - is the annual rate of return on a day by day basis. Next, we define as a measure of the financial securities risk in the inter-banking market, the standard deviation of return of those assets. The same measure was used by Tobin. [Tobin (1967)]. In table 1-1 we can observe that these assets have a different value from zero risk. In order to determine the riskless asset average rate of return, we will go to make the next judgment. Free risk rate is actually the rate of return of a financial security which has, by definition, a zero risk. But for placing it in the risk-return coordinates, this security must have a zero standard deviation and the rate of return situated on CML (considering that the market is in equilibrium) similarly with the financial assets described previously (BUBOR and BUBID)

.

We also know that BUBID rate defines a passive interest rate, paid by a bank for the attracted deposits, but from the financial investor point of view, BUBID can be considered as the lending rate of return. The average BUBID rates will determine the riskless lending rate (RFRd). The average BUBOR rates can be calculated using the daily BUBOR rates, which are active interest rates, received by a bank for a granted credit, or for a financial investor BUBOR is the borrowing rate of return. The average BUBOR rates will determine the riskless borrowing rate (RFRi).In conclusion BUBOR and BUBID rates will be used as benchmark for the values RFRd and respectively RFRi. In the MPT, borrowing means the issuance of financial securities, whereas lending means purchasing those securities. Consequently the lender is an investor that purchases the riskfree asset, whereas the borrower is issuing the riskless security. In the lending case, we will consider the free risk asset as a deposit with an equal rate of return with the pure interest rate RFRd, and a zero standard deviation of return. In the issuing case, the free risk security is a borrowing with an estimated rate of return RFRi, and likewise the risk, measured by the standard deviation of return, has a zero value. Holding the riskless financial security, or purchasing it, means a positive proportion in the lender portfolio. Issuing a riskfree financial security represents a negative proportion in the borrower portfolio. Appling the previous described algorithm resulted the following dates presented in table 1-1. Table 1A¢â‚¬‘1 Nr. Denomination Average RAP

Annual average rate

VarAP StDev

Annual StDev

1 BUBOR ON 0,1001% 27,77% 0,000006% 0,0245% 0,38% 2 BUBOR TM 0,1001% 27,77% 0,000006% 0,0245% 0,38% 3 BUBOR 1W 0,1020% 28,36% 0,000006% 0,0238% 0,37% 4 BUBOR 1M 0,1028% 28,63% 0,000005% 0,0233% 0,36% 5 BUBOR 3M 0,1034% 28,80% 0,000006% 0,0241% 0,38% 6 BUBOR 6M 0,1039% 28,96% 0,000007% 0,0260% 0,41% 7 BUBOR 9M 0,1046% 29,20% 0,000008% 0,0277% 0,43% 8 BUBOR 12M 0,1053% 29,40% 0,000008% 0,0288% 0,45%

RFRi

0,086%

23,44%

0,0000%

0,00%

1 BUBID ON 0,0771% 20,79% 0,000006% 0,0252% 0,40% 2 BUBID TM 0,0791% 21,38% 0,000005% 0,0220% 0,34% 3 BUBID 1W 0,0837% 22,74% 0,000005% 0,0222% 0,35% 4 BUBID 1M 0,0875% 23,90% 0,000005% 0,0225% 0,35% 5 BUBID 3M 0,0874% 23,86% 0,000006% 0,0238% 0,37% 5 BUBID 6M 0,0874% 23,86% 0,000007% 0,0259% 0,41% 7 BUBID 9M 0,0876% 23,94% 0,000007% 0,0267% 0,42% 8 BUBID 12M 0,0879% 24,01% 0,000008% 0,0278% 0,44%

RFRd

0,068%

18,12%

0,0000%

0,00%

Figure. 1A¢â‚¬‘1 For the AP period, I applied all these considerations, and as a consequence, I determined for the lending riskless rate (RFRd) an average daily value 0,068%, and an annual value 18,12%. For the borrowing riskless rate (RFRi) I obtained a value of 0,086% for the daily average rate, and 23,44% for the annual value. The values and the calculation method can be observed in figure 1-1. To determine the RFRd value I constructed a regression line (CML) for the BUBOR daily average rates of return, and for RFRi value a second regression line for the BUBID daily average rates of return. The values of the riskfree rate are presented also in the equations of the two CML lines. _Ec.-1.2 In _Ec-1.2 is written the general equation for CML, where Rp is y from the figure 1.1, RFRi equals 0,086%, =66,21% and x is and similarly for the second line.

. BET-C capital asset, and the currency assets EURO and DOLAR

In order to realize a comparison of the free risk rate of return with other financial assets rates, I defined, in the same frame of risk-return coordinates, two currency assets: EURO and DOLAR. The rate of return of these two securities was determined by adding the return of the exchange rate evolution and the BUBID ON rate of interest (Ec. 2-1). In other words, we considered that the currency market is liquid, there are no transactions costs, and the financial securities find immediate the investment possibility. In our case, once there where transactions, DOLAR and EURO assets will be lend at a BUBID ON rate. Figure. 2A¢â‚¬‘2 The daily rates of return of EURO and DOLAR where calculated as follows: _Ec. 2A¢â‚¬‘2 where : is the daily rate ROL/EURO Table 2.1 shows the values for the rates of return and risk obtained for the AP period. Table 2A¢â‚¬‘2 Nr. Denomination Average RAP

Annual Average Rate

VarAP StDev

Annual StDev

1 EURO 0,16%

48,94%

0,0035% 0,59%

9,20%

2 DOLAR 0,10%

28,61%

0,0011% 0,33%

5,22%

Figure. 2A¢â‚¬‘3 Using the same method we defined the average rate of return and the risk of BET-C. For the analyze period AP, its average annual rate of return is 58,76%, and the annual standard deviation is 23,31%. Analyzing figure 3-1 and 1-1 we can conclude that the currency assets have a greater risk than the monetary assets BUBOR and BUBID, but in the same time less then BET-C, the representative for the capital market portfolio.

Conclusion

The method described above, for determining the riskless rate of return on a emerging capital market as the Romanian market is, provides a rapid and exact measure and can be successfully used in the portfolio analyze and selection and for evaluation of portfolio performance. The free risk rate method generates in the same time the lending riskless rate and the borrowing free risk rate, both used by the CAPM analysts for determining the efficient portfolio. We demonstrated using the risk-return space that the currency assets EURO and DOLAR have a greater return than the riskless asset and the monetary assets BUBOR and BUBID and less than BET-C. But in the same time they have a greater risk than the monetary assets and less than BET-C. That is in fact the case in any functioning capital market: the financial securities are safer, but with less expected return than the capital assets. This algorithm was applied for the capital market analyse I realised for the philosophe doctor degree thezis.[Adrian NiA…A£u (2004)]. The results where realistic, and provided a verry good forecast of the Romanian capital market.

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