Risk Management Basics

- Derivatives Basics
- Put-Call Parity
- Forwards vs Futures
- Forward Rate Formula
- Cash Settlement vs Physical Settlement
- Backwardation vs Contango
- Residual Risk
- Best Futures Books
- Futures vs Options
- What are Options in Finance?
- Options Trading Strategies
- Call Options vs Put Options
- Options vs Warrants
- Writing Call Options
- Writing Put Options
- Gamma of an Option
- Hedging
- Options Trading Books
- International Option Exchanges
- Interest Rate Derivatives
- Interest Rate Swap
- Random vs Systematic ErrorÂ
- Equity Strategies
- Swaps in Finance
- Embedded Derivatives
- Commodity Derivatives
- Commodity Risk Management
- Managed Futures Strategy
- Top 7 Best Books on Derivatives
- Structured Finance Jobs
- Commodities Trading Books
- Best Commodities Books

- Fixed Income
- Equity Research vs Credit Research - Know the difference!
- Credit Analysis | What Credit Analyst Look for? 5 C's | Ratios
- Yield Curve Slope, Theory, Charts, Analysis (Complete Guide)
- Bond Pricing
- Coupon Bond
- Coupon Bond Formula
- Zero Coupon Bond
- Duration Formula
- Coupon Rate Formula
- Carrying Value of Bond
- Sinking Fund Formula
- Coupon Rate of a Bond
- Treasury Bills vs Bonds
- Coupon vs Yield
- Coupon Rate vs Interest Rate
- Credit Rating Process | A Complete Beginner's Guide
- Asset Backed Securities (RMBS, CMBS, CDOs)
- Loss Given Default - LGD | Examples, Formula, Calculation
- Top 7 Best Fixed Income Books
- ABS and MBS Index | Complete Beginner's Guide
- Top 10 Best Treasury Management Book
- Top 10 Best Credit Research Books
- Convexity of a Bond | Formula | Duration | Calculation
- Payment in Kind Bond | PIK Definition | Interest | Example
- Subordination Debt | Meaning | Example | Types | Risks
- Top 10 Best Books - Bonds Market, Bond Trading, Bond Investing
- Bonds vs Debentures
- Secured vs Unsecured Loan
- Bills of Exchange vs Promissory Note
- Bills of Exchange | Meaning | Examples | Top Features
- Promissory Notes
- Secured Loans
- Unsecured Loans
- Bonds
- Hypothecation
- Subordinated Debt
- Fallen Angel
- Bond Equivalent Yield Formula
- Junior Tranche
- Credit Analyst Interview Questions and Answers
- Debt Covenants | Bond Covenant Examples | Positive & Negative
- Credit Analyst Career
- Negative Covenants (Restrictive)
- Sinking Fund
- Bond Sinking Fund
- Negotiable Instruments
- Credit Spread
- Bond Pricing Formula

- Risk Management Careers
- Complete Beginner's Guide to CRM Exam
- How to Become a Quantitative Financial Analyst
- Risk Management Certifications and Salary
- Financial Engineering Career Guide: Program, Jobs, Salary
- Quantitative Analyst Salary | Skills | Trends | Top Employers
- Certificate in Quantitative Finance (CQF) Exam Guide
- Relative Risk Reduction Formula

- Bonds Yield and Interest Rate Risks
- Yield Curves
- Yield Curve Slope
- Term Structure of Interest Rates
- Shifts and Twists
- Conclusion

## Bonds Yield and Interest Rate Risks

Before diving into it, I presume you must be knowing what a bond is. If you don’t, a bond is a paper/document signifying a loan taken by the issuer of the bond. Since a loan is taken, the issuer pays a rate of interest on the bond’s principal known as coupon rate and the rate of return that the bondholder (lender) would make over the life of the bond is known as the yield to maturity (YTM) or the bond’s yield. You can google more about the basics of bonds like par bonds, discount bonds etc. and get back to this article.

The second point to note is that bond prices and their yields in most cases move in the opposite direction. This is a fundamental principle which governs bond markets assuming all other things equal. Imagine you hold a bond which pays you a 10% coupon and yields or returns 10% over the tenor (par bond). If market interest rates rise, the yield on bonds will also rise since participants would demand a higher return. Bonds issued by similar issuers would start yielding say 12%. Thus the bond you hold returns lesser than equivalent new issues which reduces demand for the bonds you hold yielding 10% and some may even sell these bonds and put the money into the 12% yielding bonds. This reduces the price of the bond you hold which occurred due to an increase in yields. This price fall pushes your bond’s yield to 12% thus bringing it in line with the market. Using similar logic, try understanding why a bond’s price would rise if yields fall. This price fall and price rise due to changes in interest rates (depending on the initial position taken whether you’ve bought or sold the bond short) is known as ‘price risk or interest rate risk’.

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### Yield Curve

A yield curve is a plot of bond yields of a particular issuer on the vertical axis (Y-axis) against various tenors/maturities on the horizontal axis (X-axis). But in general when you hear market ‘experts’ talk about the yield curve, reference is made to the government bond’s yield curve. Taking about corporate bond yield curves are mentioned specifically. The government issues bonds majorly to finance their budget deficit. Below is a plot of the Italian and Spanish government bonds’ yield curve aka sovereign yield curve on the mentioned date. Searching yield curves on the internet isn’t that difficult either.

Source: Bloomberg.com

The government issues bonds of various tenors. Some may be really short term and some may be really long term. The shortest tenor bonds are generally called T-Bills (where ‘T’ stands for Treasury) which have a maturity lesser than a year. T-Notes are generally those with maturities from 1 year to 10 years (2 year, 5 year, 10 year are some common T-Note issuances). T-Bonds are generally those with the longest maturity but depend on how it is generally classified in a nation. Generally bonds with maturities greater than 10 years are considered T-Bonds (15 year, 20 year, 30 year, 50 year are some common T-Bond issuances). Sometimes the 10 year bond is also considered to be a T-Bond.

**So what is the conclusion?** These terms are used quite loosely in the market and not much importance is given to how we refer to them. It is subjective and doesn’t really matter much unless we totally screw it up – you can’t call a T-Bill as a T-Bond even by mistake. That would be a disaster of sorts! But people can say that the 5 year or whichever year’s bond is yielding x%.

To get the specifics right one generally says that, “the 10 year USTs (US Treasury)/ the 10 year benchmarks are yielding 1.50% or the 10 year BTPs (Italian bonds) are yielding 1.14% or the 5 year UK Gilts are at 0.20%” for example.

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source: money.net

Given this basic understanding of what a yield curve is, we can also term the yield curve differently – the difference in yields between the highest tenor bond and the lowest tenor bond. Right? Here is the subjective part of it – the highest tenor bond depends on the liquidity, commonality among market participants, a respectable tenor and other factors. For example

earlier, one would term the US yield curve as the difference between the 30 year and 2-year yields. Now one terms it as the difference between the 10 year and the 2-year yields. That’s how it has evolved. Obviously, in this case, the graph would look different since it is a spread between say, the 2 year and the 10-year yields.

### Yield Curve Slope

The graph earlier and almost any other yield curve’s graph you see would look ‘upward sloping’.

#### Upward Slope Yield Curve

The reason is simple – longer the tenor, the riskier it is. If you take a 2-year bank loan you would have to pay a lower rate of interest than a 5-year loan, which would be lesser than that of a 10-year loan. The same is applicable to bonds since they are essentially loans – term premium. This is also an indicator of the soundness of an economy. An upward slope yield curve indicates that the economy may be functioning normally. The steeper the curve is, the impression is that the economy is normal and not in a recession like a scenario anytime soon. Why the curve indicate the position of the economy? The government runs the country and the economy along with the respective Central Bank which are also part of the government.

source: treasury.gov

The rates at which they borrow are generally riskless and interest rates charged to other participants in the economy like institutions and individuals are determined over and above these rates due to the borrower’s inherent risk of not paying back etc. i.e., a spread over the government’s borrowing rates are added.

#### Flat / Inverted Yield Curve

If the curve is flat or inverted, it could indicate that the economy may either be in a recession or close to one. Imagine if the long rates and short rates are almost the same or that the long rates are lower than the short rates. One would obviously prefer borrowing long term as they lock in a lower rate for longer indicates that the general equation of risk between long and short rates is topsy-turvy. The longer investors are willing to borrow long term, the lower the chances of having those rates go up and lower the demand for borrowing at a higher rate in the short term. Lower the rates for long, chances are that the economy is going to move slowly for long and might slip into a recession if necessary action is not taken. The depths of these are covered in the theory of the term structure of interest rates.

source: treasury.gov

### Yield Curve’s Term Structure of Interest Rates

The term structure of interest rates talks about the expectations hypothesis, liquidity preference theory, and the market segmentation theory in general to explain the yield curve’s structure.

#### Expectations Theory

- This is also called as the ‘Pure Expectations Theory’. This theory says that long rates are a tool to help forecast future short rates.
- If the 1 year rate today is at 1%, and the 2 year rate is 2% then the one year rate after one year (1yr 1yr forward rate) is around 3% [1.02^2/1.01^1 A simple average would do well for an approximation => (1% + x%)/2 = 2% and solve for x].
- So, you would get the same return if you invest in a two-year bond as you would in two one year bonds (a one year bond today and rolling it over in a one year bond after one year).

The limitation of this theory is that future short rates may differ from what is calculated, and other factors also influence long rates like expected inflation. In general, the short term rates are influenced the most by Central Bank policy rate changes and long term rates are influenced the most by expected inflation. Secondly, it assumes that investors are indifferent to investing in bonds of different maturities since it looks like the risk is the same. An upward slope yield curve implies that short-term rates would continue rising, a flat curve implies that rates could either stay flat or rise and a downward slope curve implies that rates would continue falling.

#### Liquidity Preference Theory

- This theory essentially says that investors are biased towards investing in short term bonds. Why? As mentioned earlier, long term bonds are riskier than short term ones because of the amount of time that the money has been committed.
- Since bond prices and yields move inversely, intuitively due to the higher risk in a long term bond the price change due to changes in yields would be heavier than the price change of a short term bond.
- So, to buy a long term bond, the investor would expect compensation much higher than the short term bond apart from the credit risk of the issuer.
- The investor may not hold a bond till maturity and faces price risk if yields go up where he would have to sell the bond cheaper before maturity. Next holding the bond for a long period may not be feasible since the bond may not be liquid – it might not be easy to sell the bond in the first place if yields go down to the benefit of the bond holder!
- Thus the compensation for price risk which also shows due to liquidity risk is what this theory is about. Hence the investor requires a yield premium relative to short term bonds for he mentioned the risk to be incentivized to hold long term bonds.

An upward slope yield curve implies that short-term rates could either go up, stay flat or go down. Why? It depends on liquidity. If liquidity is tight, rates would go up and if it’s loose, rates would go down or stay flat. But the yield premium that a long term bond commands should increase to make the curve upward slope soon. A flat curve and an inverted curve would imply falling short rates.

#### Market Segmentation Theory

- This theory is based on demand and supply dynamics of different maturity segments of bonds – short term, medium term, and long term.
- The supply and demand of bonds of particular maturity segments are what drives its yields.
- Higher supply/lower demand implies higher yields and lower supply/higher demand implies lower yields.
- It is also important to note that the demand and supply of bonds are also based upon yields i.e., different yields can imply altering the demand and supply of bonds.

#### Preferred Habitat Theory

- This is an offshoot of the Market Segmentation Theory which says that investors may move out their preferred specific maturity segments if the risk-reward equation suits their purpose and helps match their liabilities.
- In other words, if the yield differentials in bonds outside their preferred/general maturity segments benefit them, then investors would put their money into those bonds.
- In the Market Segmentation Theory, the curve can have any shape as it ultimately depends on where investors want to put their money to work.
- Even if many investors regularly deal with 10-year bonds, if they find that 5-year bonds are cheap, then they will accumulate into it.

### Shifts and Twists

This is just a brief introduction into yield curve moves and shapes. You already know the shapes – upward sloping (steep), downward sloping (inverted) and flat. These are part of yield curve moves. So let us look at the moves:

- If all the tenors’ yields move by the same amount, then the shift in the curve is called a ‘parallel shift’. Eg. The 1y, 2y, 5y, 10y, 15y, 20y and 30y yields all move ± 0.5%.

- If all the tenors’ yields do not move by the same amount, then the shift in the curve is called a ‘non-parallel shift’.

#### Non-Parallel Shifts

**Twists**

A steep curve (wide spread between long rates and short rates) or a flat curve (thin spread between long rates and short rates).

**Butterfly**

While twists and parallel shifts generally talk about straight moves, a butterfly is about the curvature. A butterfly is a humped shape curve. Short and long rates are lower than the middle rates.

**Positive Butterfly:**When the butterfly lessens its curvature and becomes flatter. The hump becomes less humped. The short, middle and long rates are tending towards the same rate where the short and long rates rise more or fall less and/or the middle rate falls more or rises less causing a positive butterfly.

**Negative Butterfly:**When the butterfly increases its curvature and becomes even more humped. The short and long rates fall more or rise less and/or the middle rate rises more or fall less causing a negative butterfly.

### Conclusion

For obvious reasons, I haven’t put pictures of the different butterfly shifts or steep curves or flat curves and so on because you should picture it and start thinking what likely trades you could put on if you expected each of them to happen in the future.

Yield curves as mentioned early on are generally government bond yield curves. But there are also corporate issuer’s yield curves, credit rating based yield curves, LIBOR curves, OIS curve, swap curves (which are a type of yield curve) and several other types of curves which haven’t been touched upon. Another variant of yield curves is spot curves, par curves, forward curves, etc. Hope you got some clarity on yield curve basics. If you have, you should partly be able to understand what ‘experts’ talk about regarding yield curves.

Jonah Stephano says

Excellent Blog. I must appreciate your hard work, all the time you try to bring something new to readers and you actually bring that in a such a brilliant way that must be appreciated. Although I have only one question. Can you tell me what is Yield Spread?

Dheeraj Vaidya says

: Thanks for you appreciation. This means a lot! Yield spread is nothing but a credit spread and it is simply the difference between two bonds. Basically, it’s the difference of rate of returns of two varied investments which are quoted mostly of different quality. Mostly this is used by bond investors to measure how expensive or cheap a specific bond is. Hope this was Helpful!

Shawn Critchon says

Very Insightful. Thanks for sharing this informative blog.

Dheeraj Vaidya says

thanks Shawn!