Risk (Duration, Convexity, Vol)

Question 1

Macaulay Duration step by step
Conclusions of Macaulay (Lowert and higher)

What does it tells us?

Answer 1

1. Every CF on PV
2. Sum of all CF = Price
3. Weigh all PV
   ——–
   Price
4. Sum every weighted PV, Weighted by the years!

Higher the Copoun, LOWER macauley (more reinvestment risk)
Lower maturity, LOWER macauley

It tells us the exactly moment that the price risk and the reinvestment risk offset

Question 2

ModDur =

What it tells us?

Formula of % price change with duration

Approx. Mod Dur and Effect Dur =

Answer 2

1. ## maculey(1+YTM)

% bonds price in 1% change in YTM
(-duration)(Change YTM)

2.

Question 3

3 conditions to YTM = E(R)

Answer 3

1. No default
2. Carry to maturity
3. Reinvestment Rate = YTM

Question 4

What is the best of duration calculation method for Options Bonds?

Is a Effective Duration os a putable bond is less than option-free:?

Answer 4

1.Effective Duration

2.Yes.
The put works like a floor. When yield increases, the price doesnt fall below put.
So Effective Duration is less than option-free

Question 5

Sources of return in a bond: (3)

Answer 5

1. Coupon payment
   2.Capital gain or losses (Prior to maturity)
2. Reinvestment interest on coupon Payments

Question 6

Overestimation and underestimation of price with DURATION.
why is it occurs?

What happens with the price, when you consider Convexity?

Answer 6

1. Overestimate DECREASE IN PRICE with increase in yield

Underestimate INCREASE IN PRICE with decreased yield.

It occurs because duration is a linear relation which does not consider convexity

2. Considering convexting

Ex. Oprtion free bond ( + Positve convex)

⬇️ Yield — ⬆️ Increase Price >⬇️ Decrease in price