Bond Guru

Zeros have higher "promised" YTMs because they have higher risk (because of the higher durations) and tax disadvantages (you don't get any interest, but you have to pay taxes on the imputed income annually). Firms get the interest deduction even though there is no corresponding cash flow from interest expense. Also, zeros are worth more when rates decline because there's no reinvestment risk and no commissions to pay on reinvested coupons.

Deferred coupons: Deferred interest, Step-up bonds, Payment in kind.

Munis that are issued at par and have coupons are called muni multipliers. If they can get revenue from 2 sources- they're called double barreled. Muni insurance cannot be canceled once purchased (what's the point?).

Coupon less than required yield- bonds sells at less than par (discount). Bonds at par or at a slight discount will have less price volatility than deep discounts or premiums. So bonds with coupons close to market rates will be valued higher.

Bond risk: Systematic: Rate. Unsystematic: Reinvestment, Default (Sector spread), Call, Inflation, Exchange rate, and Volatility. Call risk: When market rates come down, price of an outstanding bond won't go up as much. It will be "compressed" to converge with the call price (this is the point on the price/yield curve where the price stops going up with decreases in yield. This new part of the curve is negatively convex). Less restrictive bond indentures and enhancing shareholder wealth are event risks. Convertible bonds are not usually secured by company assets. Investors are compensated for these risks with higher coupons.

Bond prices move inversely with interest rates because the PVs of the cash flows are discounted back to the present at a lower/higher rates. Given unchanged cash flows, the lower the rate use for discounting, the higher the PV. Price volatility is greater the lower the coupon rate, lower YTM, and longer the maturity.

DURATION:

7 kinds in total: Raw, Macaulay, Modified, Dollar, Option adjusted, Effective, and Partial.

2 main kinds: Macaulay and Modified. Each is a linear relationship. But actual large price changes are convex, not linear (that's why convexity is the 2nd order calculation).

Macaulay duration: The effective maturity (?) or the average life of a bond. The average term of a bond's maturity, weighted by the PV of cash flows. In other word's it's the average length of time a bond is outstanding, or when you really break even and get your money back. For a zero, it's equal to its maturity. It's calculated by discounting each weighted cash flow to the present, then summing them all up. Then divide this sum by the bond's current price. It quantifies the combined impact of coupon rate, current market price, and maturity.

Modified duration (MD): The percentage price change for a 100 bp change in current market yield. It's the best way to approximate the percentage change in price for a given change in yield. It is positive for all option free bonds. It measures a bond's interest rate sensitivity and exposure to interest rates.

Considers size and timing of coupons, and YTM based on current YTMs.

It's the approximate dollar change for a small change in required yield. Modified duration is always less than Macaulay by about 4-6%. An assumption is that cash flows don't change when interest rates change (so you can't use regular duration with MBSs).

Properties of duration:

> The lower the coupon rate, the higher the duration (takes longer to get your money back).

> The lower the current interest rate environment- the lower the duration. The duration of a bond (selling at a premium) will increase if rates decline. When rates fall, duration is expected to increase because the coupons are assumed to be reinvested at market rates.

> A lower duration means less price appreciation when rates fall.

> Duration will overestimate the decline in price change when rates rise by the difference between the linear duration curve and convexity curve (the price really didn't fall by that much). Duration will underestimate the increase in price when rates fall. The error is greater for falling rates than for an increase in rates. Both errors make the change in price favorable because prices rise more and fall less than duration alone.

> Regular duration & convexity both assume the yield curve is flat and only parallel shifts are possible and only work for option free bonds!

> The steeper the duration tangent line, the greater the duration, and vice versa.

> Because of duration, investors are able to construct immunized portfolios that ensures returns over a target holding period.

> As yields increase (decrease) the dollar duration decreases (increases) for both market rates and existing coupons.

Problems with duration: > Assumes reinvestment rate is the same throughout the bond's life.

> Assumes yield curve changes will always be flat and that any shifts will be parallel

(except for partial).

> MD doesn't work well on bonds with options.

> It's not very accurate for large yield changes (that’s why you have to add convexity).