## Corporate bond ratings

Bonds are given ratings depending on the worthiness of its credit value. During this process, letters that normally range from AAA to C are assigned to the bonds expressing these credit ratings or credit-quality for investments. The highest credit-quality grade is normally given the letters AAA where as BBB expresses the average credit quality. C represents junk bonds or those bonds that do not attract any investment grade and having low credit quality (Domash, 2009). Bonds with high ratings usually take longer time to mature and therefore more risky that those with lower grades. Because of their high riskiness they are also being issued at high interest rates thus attracting higher returns or yields.

Accordingly if W bonds are rated AAA meaning that it has longer time to mature and therefore have higher risks thus attracting higher interest rates. X is rated BBB hence having average interest rates as compared to W and therefore W will be rated higher that X in terms of interest rates. But those bonds that take shorter periods to mature usually have low risks and therefore low interest rates or yields to maturity thus Y which is a bond that takes a shorter time to mature than W and X will be given lower rate. The liquidity of the market increases the risks that the investors are likely to encounter thereby attracting higher interest rates (Domash, 2009). Thus bond Z that has the same maturity as bond Y but operates in a more liquid market will have higher interest rates than Y and therefore would be rated higher in terms of interest rate earnings. In terms of yield to maturity, the bonds will be rated from the highest to the lowest as follows W, X, Z and Y respectively.

## The yield curve

Yield curves show the relationship between the yield to maturities and the equivalent dates of treasury secured fixed-income maturities bench mark. The reason why treasury securities are used as a benchmark is because they are considered risk free. Investors normally use yield curves to measure the direction of the future interest rates depending on the status of the economy. The difference between the earnings of the fixed-income of the corporate and treasury securities is what constitutes the credit spread (Boyes & Melvin, 2006). This is graphically represented by the gap between the slopes of the treasury securities and the corporate bonds.

Economists can easily use the credit spreads to predict the future conditions of the economy by analyzing the behavior of the credit spreads. Wider gaps between the coporporate and the treasury securities show that the economy is shrinking or is in recession. This means that companies are unlikely to borrow money at high interest rates to expand there operations thereby reducing their chances of making profits. In addition, the investors are more likely to lose their money in case the economy shrinks deeper into the recession (Boyes & Melvin, 2006). In other words shrinking economy contributes to higher risks connected to investing in the long term corporate bonds. On the other hand when the economy is expanding the interest rates declines and the credit spread narrows. The declining interest rates shows the long run expanding economy that reduces the risks involved in investing in the long term corporate bonds.

## The real return rate on a bought bond

Let us take F to be the initial principal which equals to $10,000 and the interest received to be $400. The summation of these values gives us the nominal return which= $10,400 while the nominal rate of return would be given by [400/10,000] ×100=0.04×100=4%. However, the inflation rate was 5% and this would give us a real return rate of 4% – 5%=-1%. At a glance, this seems like an individual has made $400 yet the total amount paid on the gain of $400 normally depends on the tax bracket and rate of inflation. To calculate the real worth of $10400, we must account for the inflation rate which was 5%. This usually varies from period to period. Therefore, the received nominal amount of F = $10,400 can be converted into real terms (f) by deflating it using the formula f=F/(1+ i) whereby f represents the deflated or the real amount; F is the nominal amount; and i is the inflation rate (Fabozzi, 2009). The deflated amount in real terms would be given by f=F/(1+ i)= $10,400/(1+ 0.05)=($10,400/1.05)=$9904.80. However, the real return rate (r) requires that f/F = (9904.80/10,000)/100. Hence, r =-0.0099× 100 =-0.99%

## The calculations of stock’s current yield, the return, and capital gains yield

The stock’s current yield is obtained through dividing the dividend by the stock price at the beginning of the year and this equals to $2/$50= 0.04×100=4%. Hence, 4% is the stock’s current yield.

Capital-gains yield for this stock is given by ([Ending stock Price- Beginning stock Price]/ Beginning stock Price) ×100= ([$53-$50]/50) ×100=6%. Therefore, 6% is the capital gains yield.

Based on Brigham and Houston (2008) assertions, the discount for this stock is given by subtracting the beginning stock price from the ending stock Price to obtain $3 which is gotten from $53-$50. This annualized capital gain is then added to the annual dividend paid during the year of $2 to get the annualized return of $5, which emanates from $3+$2.

## Using the capital-asset pricing model to predict stock returns

According to Brigham and Houston (2008), the capital asset pricing model if given by the formula: r_{a} =r_{f} +β_{a} (r_{m} – r_{f}) where: β_{a}= stock security beta= -0.3, 0.7, and 1.6; r_{m}= expected holding market return= 12% r_{f}= risk free rate= 2%; and (r_{m} – r_{f})= market premium equity

The expected return on a stock with beta= -0.3 will give r_{a}= [2%-0.3(12%-2%)] =-1%

The expected return on a stock with beta= 0.7 will give r_{a}= [2% +0.7 (12%-2%)] =9%

The expected return on a stock with beta= 0.7 will give r_{a}= [2% +1.6 (12%-2%)] =18%

## References

Brigham, E., F. & Houston, J., F. (2008). *Fundamentals of financial management*. Auckland, New Zealand: Cengage Learning.

Boyes, W., &, Melvin, M. (2006). *Economics*. Auckland, New Zealand: Cengage Learning.

Domash, H. (2009). *Fire Your Stock Analyst: Analyzing Stocks on Your Own*. Massachusetts, USA: FT Press.

Fabozzi, F., J. (2009). *Institutional Investment Management: Equity and Bond Portfolio Strategies and Applications*. Hoboken, New Jersey: John Wiley and Sons.