An investor has $1400 to invest, and his financial analyst recommends two types of junk bonds. The A bonds have a 6% annual yield with a default rate of 3%. The B bonds have a 9% annual yield with a default rate of 7%. (If the bond defaults, the $1400 is lost.) Which of the two bonds is better? Why? Should he select either bond? Why or why not?
To determine which bond is better, we need to compare the expected returns for both A and B bonds.
Let's start with the A bonds:
- The yield on A bonds is 6% annually, so the return on investment would be $1400 * 0.06 = $84 per year.
- The default rate for A bonds is 3%, which means there is a 3% chance of losing the entire investment, resulting in a loss of $1400.
So, the expected return for A bonds can be calculated as:
Expected return = (1 - default rate) * yield = (1 - 0.03) * 0.06 = 0.97 * 0.06 = 0.0582 or 5.82%.
Now let's calculate the expected return for B bonds:
- The yield on B bonds is 9% annually, so the return on investment would be $1400 * 0.09 = $126 per year.
- The default rate for B bonds is 7%, which means there is a 7% chance of losing the entire investment, resulting in a loss of $1400.
So, the expected return for B bonds can be calculated as:
Expected return = (1 - default rate) * yield = (1 - 0.07) * 0.09 = 0.93 * 0.09 = 0.0837 or 8.37%.
Comparing the expected returns, we can see that the expected return for B bonds (8.37%) is higher than the expected return for A bonds (5.82%). Therefore, based on expected returns alone, B bonds seem to be the better choice.
However, it is also essential to consider the risk associated with each bond. B bonds have a higher default rate (7%) compared to A bonds (3%). This means that investing in B bonds carries a higher risk of losing the entire investment due to defaults.
Considering the risk and the expected returns, the investor needs to assess their risk tolerance. If they are comfortable with the higher risk associated with B bonds and prioritize higher expected returns, they could select B bonds. Alternatively, if they are risk-averse and want more stability, choosing A bonds might be a safer option despite the lower returns.
Ultimately, the decision depends on the investor's risk tolerance and investment goals. It's advisable to consult with a financial advisor before making any investment decisions.
To determine which bond is better, we need to compare the expected returns of the A and B bonds. The expected return takes into account both the yield and the default rate.
For the A bonds:
Yield = 6%
Default rate = 3%
Expected return = Yield - (Default rate * Investment)
Expected return = 6% - (3% * $1400)
Calculating the expected return for the A bonds:
Expected return = 6% - (0.03 * $1400) = 6% - $42 = -9.6% (negative return)
For the B bonds:
Yield = 9%
Default rate = 7%
Expected return = Yield - (Default rate * Investment)
Expected return = 9% - (7% * $1400)
Calculating the expected return for the B bonds:
Expected return = 9% - (0.07 * $1400) = 9% - $98 = -89.6% (negative return)
Comparing the expected returns, both bonds have negative returns, indicating that there is a higher likelihood of losing money rather than gaining. Therefore, based on the given information, neither bond is a good investment choice.
It's important to note that there may be other factors to consider when making investment decisions, such as the investor's risk tolerance and investment goals. It is recommended to consult with a financial advisor before making any investment decisions.