Return on Financial Assets

Return on Financial Assets

There are a number of factors that affect bond pricing. The basic bond pricing formula is as follows:

Investopedia

In this formula, the coupon payments, number of payments, interest rate and value at maturity are taken into consideration. The question at hand pertains to bonds that are the same in all characteristics except time to maturity and risk level. The risk of the bond will be reflected in the interest rate and the time to maturity will be reflected in the number of payments remaining on the bond. Initially, it is easy to make a couple of basic assessments. The corporate bond with AAA will be rated more highly than one with BBB. This places BBB (X bond) last. With a lower time to maturity than bond W, the third bond (Y) will have a lower yield to maturity, because the shorter time to maturity will result in lower risk. Lastly, a more liquid market has a lower risk as well, so the final bond (Z) will have the lowest interest rate.

Lowest rate: Bond Z, 2nd-lowest rate: Bond Y; 2nd-highest rate Bond W, and highest rate Bond X.

2. Estrella and Mishkin (1996) argued that the spread between the rates on the 10-year Treasury note and the 3-month Treasury note (the yield curve) could be used as a predictor for U.S. recessions. Both short- and long-term rates have proven to be adequate predictors of future economic activity. When the yield curve begins to flatten, this signals expectations of a slowdown, while an inverted yield curve is a predictor of a recession. On an inverted yield curve, the short-term rates are higher than long-term rates of equivalent credit quality.

Thus, economist generally will study the yield curve and look for trends that signal if the yield curve is shifting to an inverted format. This means that the rates on long-term Treasuries are falling, indicating that the market believes that an economic slowdown will occur, stifling long-term growth. Short-term growth at this stage is still expected, because the yield curve is a predictor and the in long-term rates occurs before the actual recession.

3. To calculate the real return, we subtract the inflation rate from the gross return. The gross return in this case was 4% (400/10,000) and the inflation rate was 5%. Thus, the real return was -1%:

.04 - .05 = -0.1%

4. The current yield of the stock is $2 / $53 = 3.77% There are no expectations of capital gains on the current yield, so historical performance is irrelevant. It is assumed in this model that the dividend next year will be the same as it was the previous year, and this expected dividend is the basis of the calculation, until the company announces what its dividend for the next year will be.

The capital gains yield on the stock was ($53-$50)/$50 = 6%

The return on the stock over the course of this year was $5 ($3 capital gain + $2 dividend). The original purchase price was $50, so $5 / $50 = 10% is the total return on the stock over the course of the past year.

5. The formula for CAPM is as follows:

source: Investopedia

In this situation, the risk-free rate has been identified as being 2%. The market risk rate is 12%, so the risk-free rate needs to be subtracted from this to derive the market risk premium. The betas for each company are given. All other factors being equal (and they are), the lower the beta the lower the expected rate of return on the stock.

For the three securities, we have CAPM calculations as follows: