Week 10 Flashcards
What is the yield curve? What is the general trend?
A graph of yield of bonds as a function of their term to maturity. Typically short maturity bonds will provide less yield than long term. This is because the longer maturity bond must match the expected return of rolling over a lower maturity bond.
What does the expectations hypothesis state?
The expectations hypothesis states that yields to maturity are determined solely by expectations of future short term interest rates. This means if interest rates are expected to go up the long maturity bonds will be more expensive, if the interest rates are expected to go down they will get cheaper.
What should our return be equal to under the expectation hypothesis for everal different maturity bonds?
Under the expectation hypothesis our return should be the same whether we take a series of 1 year bonds, or the same number of years as one bond. We can use this to calculate the yield to maturity of bonds, given we have an equivalent arrangement.
What is the short rate with reference to bonds? What about the spot rate?
The short rate(forward rate) is the one year interest rate, the spot rate is the overall yield to maturity over the investment period, which we can use as a prediction of future short rates.
What is the liquidity preference theory? What does it mean for the yield curve?
The liquidity preference theory states that long-term bonds are more risky, this suggests the forward rate should be higher than the expected future forward rate, this excess of the forward rate over the expected rate is the liquidity premium and is predicted to be positive.
The yield curve has an upward bias built into the long-term rates because of this liquidity premium.
What does the yield curve typically reflect, what can it be a sign of?
The yield curve reflects expectations of future interest rates, these forecasts of future rates however can be clouded by other factors, such as liquidity premiums. If the yield to maturity increases as maturity date increases then investors expect interest rates to increase, if it decreases the interest rate is expected to fall, hence it is a sign of recession fears.
What is a bond’s interest rate sensitivity? What factors is it related to?
The interest rate sensitivity details the change in bond price as a function of yield to maturity.
Factors:
- There is an inverse relationship between bond price and yield
- An increase in bond yield to maturity results in a smaller price decline than the gain associated with an equivalent yield of equal magnitude.
- Long-term bonds tend to be more price sensitive to interest rate changes than short-term bonds
- As maturity increases, price sensitivity increases slower, the interest rate risk is less than proportional to bond maturity.
- Price sensitivity is inversely related to the coupon rate.
- Price sensitivity is inversely related to the yield to maturity at which the bond is currently selling.
What is a bond’s duration?
Duration is a measure of the average maturity of all bond payments.
It is the weighted average of the time until each payment is received, with weights proportional to the present value of the payment. This will be the maturity for zero coupon bonds, or less than the maturity for coupon bonds. It can help us predict how bond prices will react in response to interest rate changes.
What is a bond’s duration’s relation to coupon rate and maturity?
For a given coupon rate, a bond’s duration generally increases with maturity. For a given term to maturity and yield to maturity, the higher the coupon rate, the smaller the bond’s duration, generally.
For a given term to maturity and coupon rate, the higher the coupon rate, the smaller the bond’s duration.
What is durations relation to bond price volatility?
positively related.
What is the duration of a level perpetuity
(1+y)/y
What is the percentage change in the bond’s price as a relation to duration?
The percentatge change in the bond’s price is approximately equal to -duration * the percentage change in (1+ bond yield). This means duration * yield change approximately equals the change in price. This modified duration is particularly good if the yield change is small. It gets less accurate as the yield changes more (2% is quite large).
What is a bond’s convexity? What can we do with it to predict bond price changes?
The rate of change of the slope of the price-yield curve, expressed as a fraction of the bond price.
The change in price of a bond = -duration * change in yield + 0.5(convexitychange in yield^2).
Why is convexity useful to investors?
Investors like convexity because bonds with greater curvature gain more in price when yields fall than they lose when yields rise. Investors typically pay higher prices and accept lower yields to maturity on bonds with higher convexity.
What forms does interest rate risk come in?
Price risk, the risk than an investor cannot sell the bond for as much as anticipated, which will happen if interest rates increase,
Reinvestment risk: The risk that the investor will not be able to reinvest the coupons at the promised yield rate. A decrease in interest rates reduces the future value of the reinvested coupons.
