Financial Risk Manager Part 1

Get started today

Ultimate access to all questions.

Explanation:

Let the 6-year discount factor be:

df(6)=0.820

1) Implied continuously compounded spot rate

For continuous compounding:

df(t)=e^{-rt}

So:

r = -\frac{\ln(0.820)}{6} \approx 0.03314 = 3.314\%

2) Implied semi-annual spot rate

For semi-annual compounding:

df(t)=\frac{1}{\left(1+\frac{y}{2}\right)^{2t}}

Thus:

0.820 = \frac{1}{\left(1+\frac{y}{2}\right)^{12}}

1+\frac{y}{2} = \left(\frac{1}{0.820}\right)^{1/12}

y \approx 3.342\%

3) Difference

3.342\% - 3.314\% = 0.028\% = 2.8 \text{ bps}

The nearest answer is 2.75 basis points.

Explanation:

Let the 6-year discount factor be:

df(6)=0.820

1) Implied continuously compounded spot rate

For continuous compounding:

df(t)=e^{-rt}

So:

r = -\frac{\ln(0.820)}{6} \approx 0.03314 = 3.314\%

2) Implied semi-annual spot rate

For semi-annual compounding:

df(t)=\frac{1}{\left(1+\frac{y}{2}\right)^{2t}}

Thus:

0.820 = \frac{1}{\left(1+\frac{y}{2}\right)^{12}}

1+\frac{y}{2} = \left(\frac{1}{0.820}\right)^{1/12}

y \approx 3.342\%

3) Difference

3.342\% - 3.314\% = 0.028\% = 2.8 \text{ bps}

The nearest answer is 2.75 basis points.

Comments (0)

No comments yet.

Q-712.3. If the six-year discount factor, df(6.0), is `$0.82`0 then which of the following is nearest to the basis point difference between the implied semi-annual six-year spot rate and the implied continuously compounded six-year spot rate?

Exam-Like

Community

MManit

Last updated: April 18, 2026 at 11:32

a) Zero

33.3%

b) 2.75 basis points

50.0%

c) 30.0 basis points

8.3%

d) 249 basis points

8.3%

Financial Risk Manager Part 1

Get started today

1) Implied continuously compounded spot rate

2) Implied semi-annual spot rate

3) Difference

1) Implied continuously compounded spot rate

2) Implied semi-annual spot rate

3) Difference

Comments (0)

Get started today

Comments (0)

Q-712.3. If the six-year discount factor, df(6.0), is $0.820 then which of the following is nearest to the basis point difference between the implied semi-annual six-year spot rate and the implied continuously compounded six-year spot rate?

Q-712.3. If the six-year discount factor, df(6.0), is `$0.82`0 then which of the following is nearest to the basis point difference between the implied semi-annual six-year spot rate and the implied continuously compounded six-year spot rate?