Mechanic

According to the pure expectations theory, which of the following statements is most accurate? Forward rates:

A) exclusively represent expected future spot rates.

B) are biased estimates of market expectations.

C) always overestimate future spot rates.

---

The pure expectations theory, also referred to as the unbiased expectations theory, purports that forward rates are solely a function of expected future spot rates. Under the pure expectations theory, a yield curve that is upward (downward) sloping, means that short-term rates are expected to rise (fall). A flat yield curve implies that the market expects short-term rates to remain constant.

spartan1

What are the implications for the shape of the yield curve according to the liquidity theory? The yield curve:

A) must be upward sloping.

B) is always flat.

C) may have any shape.

---

The liquidity theory holds that investors demand a premium to compensate them to interest rate exposure and the premium increases with maturity. Even after adding the premium to a steep downward sloping yield curve the result will still be downward sloping.

spartan1

The liquidity premium theory of the term structure of interest rates projects that the normal shape of the yield curve will be:

A) upward sloping.

B) variable.

C) downward sloping.

---

The liquidity theory holds that investors demand a premium to compensate them to interest rate exposure and the premium increases with maturity. By itself, the liquidity theory implies an upward sloping yield curve.

spartan1

What adjustment must be made to the key rate durations to measure the risk of a steepening of an already upward sloping yield curve?

A) Increase all key rates by the same amount.

B) Increase the key rates at the short end of the yield curve.

C) Decrease the key rates at the short end of the yield curve.

---

Decreasing the key rates at the short end of the yield curve makes an upward sloping yield curve steeper. Performing the corresponding change in portfolio value will determine the risk of a steepening yield curve.

spartan1

Which of the following best describes key rate duration? Key rate duration is determined by:

A) changing the curvature of the entire yield curve.

B) changing the yield of a specific maturity.

C) shifting the whole yield curve in a parallel manner.

---

Key rate duration can be defined as the approximate percentage change in the value of a bond or bond portfolio in response to a 100 basis point change in a key rate, holding all other rates constant, where every security or portfolio has a set of key rate durations, one for each key rate maturity point.

spartan1

Which of the following is closest to the annualized yield volatility (250 trading days per year) if the daily yield volatility is equal to 0.45%?

A) 7.12%.

B) 9.73%.

C) 112.50%.

---

Annualized yield volatility = σ ×
where:
σ = the daily yield volatility
So, annualized yield volatility = (0.45%) = 7.12%.

spartan1

Suppose that the sample mean of 25 daily yield changes is 0.08%, and the sum of the squared deviations from the mean is 9.6464. Which of the following is the closest to the daily yield volatility?

A) 0.6340%.

B) 0.4019%.

C) 0.3859%.

---

Daily yield volatility is the standard deviation of the daily yield changes. The variance is obtained by dividing the sum of the squared deviations by the number of observations minus one. Therefore, we have:
Variance = 9.6464/(25 – 1) = 0.4019
Standard deviation = yield volatility = (0.4019)½ = 0.6340%

spartan1

Which of the following is closest to the annualized yield volatility (250 trading days per year) if the daily yield volatility is equal to 0.6754%?

A) 10.68%.

B) 9.73%.

C) 168.85%.

---

Annualized yield volatility = σ ×
where:
σ = the daily yield volatility
So, annualized yield volatility = (0.6754%) = 10.68%.

spartan1

For a given three-day period, the interest rates are 4.0%, 4.1%, and 4.0%. What is the yield volatility over this period?

A) 0.0349.

B) 0.0577.

C) 0.0000.

---

The yield volatility is the standard deviation of the natural logarithms of the two ratios (4.1/4.0) and (4.0/4.1) which are 0.0247 and –0.0247 respectively. Since the mean of these two numbers is zero, the standard deviation is simply {[(0.0247)2 +(-0.0247)2]/(2-1)}0.5=0.0349.

spartan1

Which of the following is the most important consideration in determining the number of observations to use to estimate the yield volatility?

A) The liquidity of the underlying instrument.

B) The shape of the yield curve.

C) The appropriate time horizon.

---

The appropriate number of days depends on the investment horizon of the user of the volatility measurement, e.g., day traders versus pension fund managers.