BONDS Flashcards
Bond prices
the present value of the coupons and the face value discounted at the rate.
P0 = SUMM(Ct/(1+rate)^t) + FV/(1+rate)^T
the interest rate y (Yield to maturity)
equates the bond price to the present value = yield to maturity
current yield
C.Y = coupon/Po
acrued interest
if bonds are bough in between coupon payments the seller is entitled to recieve a pro-rata part of the next coupon
the sale price = flat price + acrued interest
accruedinterest = annual coupon payment/2 X days since last coupon/days between coupons
if P0 > FV
bond sells at a premium and y<c
if P0 = FV
bond sells at par y=c
P0 < FV
bond sells at a dicount y>c
yield 2 maturity
measure of total retuen that the investor obtains when buying th ebond today at P0 and keeping it till maturity
issues with YTM approximation
assumes investor will be able to reinvest each coupon recieved at rate y throughout bond life
what does the upward sloping yield curve mean
yields on longer-term bonds are higher than the yields on shorter-term bonds of the same credit quality. In other words, as the maturity of the bond increases, the yield also increases. This is the most common shape of the yield curve.
downward sloping yield curve meaning
A downward sloping yield curve, also known as an inverted yield curve, occurs when the yields on longer-term bonds are lower than the yields on shorter-term bonds of the same credit quality. In this case, as the maturity of the bond increases, the yield decreases. An inverted yield curve is less common than an upward sloping yield curve and can be a sign of potential economic downturn.
forwrad rates
market’s expecttaion of spot rates that will prevail in future
MARKET EXPECTATIONS HYPOTHESIS
- long run rates are a geometric average of current and future short rates
- forward rate is an unbiased estimate of future short rates
- BONDS OF DIFFERENT MATURITIES ARE TREATED AS PERFECT SUBSTITUTES
- risk - neutral investors
- no transaction costs.
- no coupon payments, no defaults.
The fact that the term structure is upward sloping most of the time implies that the forward rate seems to overestimate the expected spot rate.
LIQUIDITY PREFERENCE THEORY
investors have short horizons and are risk averse
lenders demand a liquidity premium to hold long-term bonds
long term borrowers willing to compensate and gain by locking in a rate.
SEGMENTED MARKETS THEORY
- bonds of different maturities are in fact distinct and unconnected markets
- each of these markets finds its equilibrium seperately
- some investors may face binding limitations in what maturities to invest in.
interpreting the term structure
expectations of increases in rates can result in a rising yield curve but the rising curve need not imply expectations of higher future rates
very steep yield curve swarn of impending rate increase
falling yield curve = recession
sensitivity to interest rate changes
long maturity bonds more sensitive
slope = average maturity
curvature = depends on cash flow distribution
duration
the negative of the elasticity of the price to 1 + the yield
VOLATILITY = DURATION/ (1+Y)
steepeners
gain from widening spread between short and long term YTM - combine a long short dated bond position with a short long-dated bond position.
flatteners
gain from shrinking spread (flattening curve)
sell short term bonds and purchase long term bonds
Convexity
duration gives an approximation of the change in bond price given the change in yield, the more curvey the yield price relationsjip, the worse the approximation - covexity accounts for this
percentage changes in the value bond
can be found using duration and convexity
duration and DV01
duration is the weighted sum of component durations
