# Fixed Income Relations

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In this post, we cover the most important relations between variables from the Fixed Income CFA L1 topic.

### Inverse relationship between interest rate and bond price

Let’s begin with some basics, namely the relationship between the market discount rate and the bond price.

Generally, there is an **inverse relationship** between interest rates and the price of a bond.

**If:**

interest rates go up the price of a bond goes down,

interest rates go down the price of the bond goes up.

**If:**

the required yield changes only a bit (it either increases or decreases a bit) the absolute value of the percentage change in the bond price will be approximately the same for both increase and decrease of the market discount rate

the required yield changes a lot the absolute value of the percentage change in the bond price will be lower if the market discount rate increases than if the discount rate decreases

### Coupon rate vs. YTM

coupon rate > YTM the bond sells **at a premium** (the bond price is higher than the par value)

coupon rate = YTM the bond sells **at par** (the bond price is equal to the par value)

coupon rate < YTM the bond sells **at a discount** (the bond price is lower than the par value)

coupons’ reinvestment rate < YTM investment's realized rate of return < YTM

coupons’ reinvestment rate > YTM investment's realized rate of return > YTM

### Callable bond vs. Putable bond

value of the callable bond **=** (value of the bond without an embedded option) **-** (value of the call option)

value of the putable bond **=** (value of the bond without an embedded option) **+** (value of the put option)

volatility of the market discount rate **increases** __call option__ value **increases** __callable bond__ value **decreases**

volatility of the market discount rate **increases** __put option__ value **increases** __putable bond__ value **increases**

### Spot curve vs. Forward curve

__spot curve__ is **upward sloping** __forward curve__ **is above the spot curve**

__spot curve__ is **downward sloping** __forward curve__ **is under the spot curve**

### Reinvestment risk vs. Market price risk

the lower the coupon rate the lower reinvestment risk

the lower the coupon rate the higher market price risk

### Bond's price change (duration only)

the greater the modified duration the greater the percentage bond price change

the lower the modified duration the lower the percentage bond price change

the greater the yield change (yield volatility) the greater the percentage bond price change

the lower the yield change (yield volatility) the lower the percentage bond price change

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