# bond math interview questions

## Let’s say we have $100 in debt with 15% in PIK. How does this flow through the three statements? Let’s assume a 20% tax rate. PIK accounting questions are very common in RX interviews because so many of the out-of-court restructurings done will involve some PIK. Note: Why is this the case? The obvious answer is because the company likely doesnt have much cash on hand (negative FCF, limited liquidity) so PIK allows them to avoid imminent cash crunches. The less obvious answer, perhaps, is that PIK allows the company to offer a much higher interest rate (in this case 15%), which current holders who may be exchanging bonds into will find enticing. So lets go through it. On the income statement (IS) you will have$15 in new interest expense in the form of newly issued debt. This creates a tax shield (another reason why you can have higher interest rate) of $3 ($15*20%). Therefore, net income is down by $12. Moving to the top of the cash flow statement (CFS) you have$12, you then add back the $15 as its a non-cash expense (thats the primary reason to do PIK!), so you have cash flow from operations up by$3.

On the balance sheet (BS) you have assets (cash) up by $3, on the liabilities side you have debt up by$15, and within shareholders equity (retained earnings) you have a $12 decrease from net income. So both sides of the equation are up by$3.

## How to Prepare for a Fixed-Income Interview

Most people immediately think of government, corporate, or municipal bonds when they hear the words “fixed income.” However, fixed-income securities can include mortgage loans and a variety of financial derivatives of interest rate, corporate, and credit products.

Typically, many fixed-income traders further specialize in handling specific types of fixed-income investments, such as government or corporate bonds. Fixed-income traders must be skilled at evaluating specific investment opportunities and be able to analyze and assess the current market and economic conditions and trends to be successful.

## 4 Answers 4 Sorted by:

Back of envelope approach:

$dP simeq frac{partial P}{partial y} times Delta y$

You know that when $y=3%$, $P=100$. So you can write

$P-100 simeq frac{partial P}{partial y} times (c-y)$

Price $simeq$ 100 + Duration x (3%-9%).

Guess a duration of around 7.0 for a 10 year bond (they would assume that you would have a feel for this number).

So I get 100 – 7 x 6 = 100 – 42 = $58. If I do this carefully assuming annual compounding then I get$61.5 which is in the same ball park. You can refine this using a second order correction but this would be an acceptable first guess that you can do without calculators.

It might be more impressive to demonstrate that you have the tools and can use them. Go to the interview with a handheld calculator. The answer is a few keystrokes away.

consider your bond initially was at par (cpn=3%~=yld_0) and now answer the question what is the price change given new yld_1=9%. for a very dirty estimate use relationship between price change vs yield change and duration (~=10).for a less dirty estimate youll need some educated guess on the level of convexity. have a look at closed formula of convexity of par bond. hope this helps.

Use Taylor Expansion to approx price changes for some variations in Yield. Guess the Duration to be less than Full maturity since its Paying coupons and go from there. First price it at Par.

Thanks for contributing an answer to Quantitative Finance Stack Exchange!

• Making statements based on opinion; back them up with references or personal experience.
• Use MathJax to format equations. MathJax reference.

## FAQ

What is a bond interview question?

Sir, you have genuinely taken me through every detail of the work and led me along my career path; I would be grateful if you could give me some time to consider it. I’d like to consider a few points of my own before providing you with an answer.

How do you answer Bond interview questions?

Face value refers to the dollar value of a financial instrument when it is issued. The face value of a bond is the price that the issuer pays at the time of maturity, also referred to as “par value.” By comparison, the face value of a stock is the price set by the issuer when the stock is first issued.

What is the face value of a bond?

A fundamental principle of bond investing is that market interest rates and bond prices generally move in opposite directions. When market interest rates rise, prices of fixed-rate bonds fall.

What happens to bond prices when interest rates rise?

A fundamental principle of bond investing is that market interest rates and bond prices generally move in opposite directions. When market interest rates rise, prices of fixed-rate bonds fall.