duration and DCF
A security has an expected return of 12% and a standard deviation of 5%. Investing in a security with an expected 12% return, an investor can expect returns to range within _ to _ about 68% of the time and within 2% to 22% about __of the time.
7% to 17%;95%
Rule of 72
72/rate of return = time for investment to double
What is considered a high correlation between two securities?
>0.8
What Does a Beta Greater Than 1.00 Indicate?
A beta greater than 1.00 indicates the stock is more volatile than the market. For example, a beta of 1.50 means the stock will rise or fall 15% if the market rises or falls by 10%.
When viewing past returns of a security, an outlier would cause the greatest distortion to A) all of these equally. B) the mean. C) the median. D) the mode.
B, the mean
How does beta differ from standard deviation?
Beta measuring only systematic risk -comparing the volatility to the market. standard deviation measures both systematic and unsystematic risk - a security's total volatility compared to its expected return, including both systematic and unsystematic risk.
What is Duration?
Duration is the weighted average time it takes for an investor to receive all cash flows (coupon payments and the principal) from a bond.
T/F When the correlation coefficient is zero, the portfolio is at its maximum diversification.
F A zero correlation means there is no predictable relationship between these assets and the rest of the portfolio.
T/F Correlation is primarily used for individual investments rather than portfolios.
F correlation is used for portfolio diversification; one does not diversify an individual asset.
What is the future value (FV) of an investment?
FV = PV × (1 + r)^n, where r is the rate of return, and n is the number of periods.
How does present value change if the expected rate of return is lower than anticipated?
If the actual return is lower than expected, the present value required to meet a future goal will be higher because the investment needs more capital to reach the same future value.
Bonds with Higher Convexity
Long-term bonds (longer maturities) Low-coupon bonds Zero-coupon bonds
What is the present value (PV)?
PV = FV ÷ (1 + r)^n
T/F The lower the correlation, the more diversified the portfolio
T
What is the risk-free rate used in alpha calculations on the exam?
The risk-free rate is the return on the 91-day (13-week) U.S. Treasury bill.
For coupon bonds, duration is always less than the bond's maturity. T/F
True
In an efficient market, bonds should be priced so that their NPV is zero. T/F
True
What is Negative Beta?
What does a negative beta (e.g., −1.2) indicate about a stock's movement?A: A negative beta means the stock moves inversely to the market. For example, if the market rises by 10%, a stock with a beta of −1.2 would fall by 12%.
Median
a middle point of a distribution
What Does a Correlation Coefficient of +1 Indicate?
a perfect positive correlation, meaning the two securities move exactly in the same direction by the same amount.
How is the arithmetic mean calculated?
adding up all the values and dividing by the number of occurrences.(average)
When comparing the arithmetic mean to the geometric mean, the ____mean will always be higher, unless all of the numbers being used are the same
arithmetic
Which is the most useful in determining the price volatility of a bond to a significant change in interest rates
convexity
Alpha Formula measures
difference between portfolio's performance to what would be expected based on its risk and the market return =Alpha=(Actual return−risk-free rate)− beta×[market return−risk-free rate]
two common examples of investments with a negative correlation that can increase the diversification of a portfolio
gold stocks, and bond
the higher the convexity
greater price increase when yields fall and a smaller decrease when yields rise (that is a good thing).
The ___ the discounted cash flow (DCF), the more valuable the investment.
higher
Range
highest - lowest
The yield to maturity of a bond reflects its
irr
If you were managing a portfolio of bonds and expected interest rates to decline (bond prices will rise), you would ____ the average duration of the portfolio. On the other hand, if you were of the opinion that interest rates were going to rise (bond prices will decline), you would want to ____ the average duration.
lengthen, shorten
the ___ a bond's duration, the more its value will change for a 1% change in interest rates; the ___ the duration, the less it will change.
longer; shorter
mid-range
max+min/2
In a normal distribution, the____ and ___ are the same; nothing is skewed.
mean and median
distributions of returns are skewed either to the left (the ___ is lower than the ____)
mean is lower than the median
test topic alert Which one had some investments that significantly outperformed the average of the other investments? The answer will be the one with the highest ___.
mean.
Mode
most frequently occurring score
discount rate
rate of return used to discount future cash flows back to their present value (market interest rate)
mean may not be an appropriate measure of central tendency for ______. The term mean by itself will always refer to the ____ mean.
skewed distributions, arithmetic
that beta is a measurement of___risk
systematic/market
Net present value (NPV)
the difference between an investment's present value and its current cost
If we find two bonds with the same duration, which one offers greater interest rate risk protection
the one with the higher convexity
why are bonds with higher convexity still attractive to investors if they are more sensitive to interest rate changes?
they benefit more from falling interest rates and are less affected by rising interest rates compared to bonds with lower convexity.
NPV is generally considered more important than IRR T/F
true
Convexity
what will happen to a bond's price as interest rates change
when does the duration equal to maturity
zero-coupon bond
Geometric Mean of a and B
√ab
