# Errata for 2019 Exam 9 Products

## Errata for Practice Exams

**PE 2 - 6 (4/30): **In the question, the leverage ratio should be “**Liabilities:Equity.**”** **

**PE 2 - 5d (4/30): **The solution should state (changes in **bold**):

For bonds selling ** below** par value: Coupon rate < current yield < yield to maturity

The coupon rate < current yield because coupon rate is based on par value and current yield is based on the ** lower** price of the bond. In turn, the YTM is

**than the current yield because it accounts for the built-in capital gain on the bond.**

*greater***PE 2 - 2c (4/29): **Clarification - This problem is set up a little differently than a normal Robbin PVI/PVE question. There are two different assumptions given to you in the problem:

Loss Reserves are posted at policy inception and undiscounted

Undiscounted loss reserve-to-surplus ratio is maintained...

Part of the reasoning is because we're also doing the Feldblum method in part a, so it makes the comparison a little better. If you weren't given those assumptions, you should definitely do it the way Robbin shows it. This is a problem like this would probably have different acceptable solutions based on assumptions specified.

**PE 1 - 2 (4/10/19): **Part f has two issues:

**Probability of ruin assumption:**It’s not specified in the problem, but since Mango bases risk loads on the probability of ruin level, VaR 99% (the 1% level) is a better assumption for setting*z*. Using 5% is probably also OK here if you give that as your assumption since it’s not explicit in the problem.**Variance calculations:**The Mango variance formula only works for independent events, which is why we can ignore the combined loss scenario and look at the HU and EQ events separately. Alternatively, we can calculate the variances using the traditional variance formula (see the updated PDF and discussion).

You can download a corrected version here: PE 1-2 (Fixed)

## Errata for Exam 9 Problem Bank

**RF BKM 9 - 6 (4/28): **Typo- In the graph, the expected market return should be 10% (not 9%).

**RF Robbin IRR - 10 a (4/15/19):** (Minor clarification) Part a is correct under the implied assumption that the underwriting profit is greater than the risk-free rate. There are some additional dynamics going on here. If the underwriter profit were less than the risk-free rate, then it looks like the IRR would increase towards the risk-free rate if surplus held increased.

**RF Goldfarb - 6 (4/7/19): **The problem should have shown an assumption stating that the variance of assets is assumed to be zero.

**RF Kreps - 4 (4/5/19): **Beta should be given as 107,600 (not 107.6) in the problem. The solotion is correct.

**RF Bodoff - 4 (4/3/19): **Part c should say: “Calculate the premium net ** expenses**…”.

**RF BKM 23 - 4 (3/24/19): **This problem is a bit confusing as it's worded. The goal for part b was to focus on the credit risk in the swap, similarly to the BKM example on this in the paper which is focused on the swap, but doesn't mention the swap dealer. This is why the spread wasn't used in the calculation in the solution.

Unfortunately, BKM doesn't show an example of the credit risk for a swap where a swap dealer and bid-ask spread is involved, so it's not exactly clear. Also, if the swap dealer takes on the credit risk then it would be the swap dealer that would be impacted by a party defaulting.

**RF Robbin IRR - 4 (3/23/19): **There is a minor error in the table on pg. 271. DAC_3 and Q_3 aren’t necessary for solving the problem and were inadvertent copies of DAC_0 and Q_0. Those numbers should just have an asterisk there because they’re unnecessary.

**RF Feldblum - 7 (3/15/19): **To match the assumption stated on the problem prompt, the investment income should only be paid at the end of each year (not mid-year at t=1.5). This changes the IRR a little. You can download a corrected version here: RF Feldblum - 7 (Fixed)

**RF Butsic - 3 (3/11/19): **There is a minor calc error for the loss reserve scenario at t=3. The top loss should be **27,440 **not 27,400. This changes the E[Loss] and EPD ratio as well as the calculation in part b. You can download a corrected version here: RF Butsic - 3 (Fixed)

**RF Robbin IRR - 3 (3/8/19): **There is a minor calc error near the end: A_1 should be 1,878.35. This affects a few other calculations. The IRR in year 2 is still 27.2%. You can download a corrected version here: RF Robbin IRR - 3 (Fixed)

Also, the paid premium at year 1 should be 1100 (not 1110) and at year 2 should be 1210. This doesn’t affect the solution.

**RF Robbin UW - 9 (3/5/19): **The second term in the final calculation should discount to year 3 (not 2) and be -217.3/(1+r)**^3**. This changes the target return to 9.8%.

**RF Coval - 5 (2/26/19): **The problem should state: “…as long as the default probability of the senior tranche in the CDO^n is ** less than **10%.”

**RF Panning - 4 (2/25/19): **The expense ratio was multiplied by the loss (not premium), which is incorrect. Instead, **the expense ratio should be 20%** and the solution still works out the same.

NOTE: If you use 30% as the expense ratio, the expense is 45M, F_2019 = 8.37M*, *F_2020 = 6.375M, F_2021+ = 15.94M and **F = 30.68M**. For part b, C = 209.76M and **TEV = 240.4M**.

**RF BKM 10 - 3 (2/25/19)**: Part a asks for the risk premium, so we should subtract off the risk-free rate from the return. The **risk premium is 6%.**

**RF BKM 11 - 1 (2/25/19)**: The problem gives the risk-free rate as 2%, but 4% is used in the solution for part a. The expected return for X should be 13.7% + 2% =** 15.7%.**

**RF BKM 15 - 4 (2/25/19)**: There is a calculation error for the year 2 spot rate. The 2-year spot rate **should be r_ 2 = 6.683%.**

*This changes the forward rate in year 3 to f_*3 = 8.13% and the present value of profit to $2,433.

**RF BKM 16 - 7 (2/25/19)**: In the problem, the value of the 2-year liability should be **$50,000** (not 500,000). This was a typo in the table.

**RF BKM 16 - 9 (2/25/19)**: Part b asks to find the difference in the two-year annualized return. The boxed answer shows the new annualized return. The **difference in the return is +0.2% **and this should be the boxed solution.

**RF BKM 7 - 5 (2/22/19)**: The problem should have a bullet point stating that **the risk free rate is 3%**.

## Errata for Exam 9 Cookbook

**Robbin IRR (4/29): **Clarification - The loss reserve formula should be based on incurred minus paid loss-to-date:

Loss Reserve = sum(Incurred loss-to-date) - sum(Paid loss-to-date)

**BKM 10 - Multifactor APT Model (3/24/19)**: In the discussion, the Fama-French Three-Factor model should have **R_it for excess return** in the front, not r_it.

**Feldblum - IRR (3/11/19)**: In the discussion section about UEPR, the alternative solution is incorrect. Because we use UEPR, we should also change the required surplus for *t* = 0. This impacts the equity flows and IRR calculation. The correct IRR is 16.2%. See the fixed recipe below (link below, updated 3/11).

**Mango - Marginal Variance Method (2/4/19)**: In the discussion after the overall risk load calculation, the sentence should say “…but **the sum of the renewal risk loads (1,836)** is greater than the overall risk load.”

**BKM 7 - Optimal Complete Portfolio (1/25/19)**: In the second paragraph of the discussion, it should state:

“Investors with higher degrees of risk aversion will allocate **less** to the optimal risky portfolio than investors with lower degrees of risk aversion.”

**BKM 16 - Duration and Convexity - Semi-Annual (1/25/19)**: The convexity formula was incorrect. In the denominator, the (1 + y/k) term should be squared (like in the BKM text). I fixed the formula and calculations. Make sure to download the fixed recipe below (link below).