Financial Markets - Fixed Income Securities Exam Questions and Answers Fully Solved Latest Version
2025
Bond Pricing - Answers Price = Present Value of future Cash Flows = PV of coupons + PV of par value.
Time Value of Money - Answers The principle that a dollar received today is worth more than a dollar
received in the future.
Determined by nominal interest rates.
Changes in interest rate determine changes in bond price. - Answers Competitive markets, securities
with same cash flows must offer the same return. If coupon rate no enough to give required return,
found in similar securities, price has to adjust accordingly.
Bond Price as function of market interest rate - Answers Non-linear and decreasing.
Interest Rate Sensitivity Determinants - Answers Maturity, Coupon, Yield to Maturity
Interest Rate Sensitivity - Answers A measure of how much the price of a fixed-income security will
fluctuate as a result of changes in the interest rate.
Macaulay Duration - Answers An estimate of a bond's interest rate sensitivity based on years until
promised cash flow will arrive. A weighted average of the years in which the bond pays it cash flows.
D = Sum of wt * t, for t = 1 ... T.
where CFt are cashflows at t, and wt given by = (1/P) * (CFt / (1+y)^t)
Macaulay Duration: wt - Answers wt is the PV of cash flow as a percentage of the bond's price.
= (1/P) * (CFt / (1+y)^t)
The sum of wt = 1.
Modified Duration Formula - Answers D* = D/(1+y)
Duration: Change in Price - Answers Change in Price = -D* * P * Change in y.
Modified Duration - Answers Help approximate absolute change in the bond price, or relative change,
due to small change in the y.
Rules for Macaulay's Duration - Answers 1. Duration of a zero coupon bond equals its time to maturity,
D = T.
2. Holding maturity constant, bond's duration is higher when coupon rate is lower.
, 3. Holding coupon rate constant, bond's duration generally increases with time to maturity.
4. Holding other factors constant, duration of coupon bond is higher when bond's yield to maturity is
lower.
5. Duration of a (level) perpetuity is equal to: 1+y/ y
Duration and Convexity - Answers P(y) is convex.
Use second derivative for better approximation.
(Change in P / P) = -D* * change in y + 1/2*convexity*(change in y)^2
Convexity Formula - Answers = 1/P * d2P/dy^2
Balance Sheet Exposure to Interest Rate Risk - Answers Pension funds have liabilities, the PV of future
pensions. Changes in IR affect value. Fund movement in assets to hedge the movement in liabilities.
Management of Interest Rate Risk: Cash Flow Matching and Dedication - Answers Consider pension fund
that needs to pay $100 million in benefits. Can invest in portfolio of zero coupon bonds. (Dedication
Strategy)
Immunise portfolio to IR movement. Cash inflows and obligations offset each other.
Not used. Too many bonds, maybe mispriced, difficult to find bonds match long-term maturities.
Management of Interest Rate Risk: Duration Matching - Answers Invest in portfolio of bonds with
duration equal to duration of liabilities, and with same PV.
Value of assets affected by IR movements same way as liabilities.
Assets = Liabilities, can always pay outflows.
Rules to obtain immunisation from Interest Rate Risk - Answers 1. Value of Bond portfolio = Value of
Liabilities
2. Duration of Assets = Duration of Liabilities
2025
Bond Pricing - Answers Price = Present Value of future Cash Flows = PV of coupons + PV of par value.
Time Value of Money - Answers The principle that a dollar received today is worth more than a dollar
received in the future.
Determined by nominal interest rates.
Changes in interest rate determine changes in bond price. - Answers Competitive markets, securities
with same cash flows must offer the same return. If coupon rate no enough to give required return,
found in similar securities, price has to adjust accordingly.
Bond Price as function of market interest rate - Answers Non-linear and decreasing.
Interest Rate Sensitivity Determinants - Answers Maturity, Coupon, Yield to Maturity
Interest Rate Sensitivity - Answers A measure of how much the price of a fixed-income security will
fluctuate as a result of changes in the interest rate.
Macaulay Duration - Answers An estimate of a bond's interest rate sensitivity based on years until
promised cash flow will arrive. A weighted average of the years in which the bond pays it cash flows.
D = Sum of wt * t, for t = 1 ... T.
where CFt are cashflows at t, and wt given by = (1/P) * (CFt / (1+y)^t)
Macaulay Duration: wt - Answers wt is the PV of cash flow as a percentage of the bond's price.
= (1/P) * (CFt / (1+y)^t)
The sum of wt = 1.
Modified Duration Formula - Answers D* = D/(1+y)
Duration: Change in Price - Answers Change in Price = -D* * P * Change in y.
Modified Duration - Answers Help approximate absolute change in the bond price, or relative change,
due to small change in the y.
Rules for Macaulay's Duration - Answers 1. Duration of a zero coupon bond equals its time to maturity,
D = T.
2. Holding maturity constant, bond's duration is higher when coupon rate is lower.
, 3. Holding coupon rate constant, bond's duration generally increases with time to maturity.
4. Holding other factors constant, duration of coupon bond is higher when bond's yield to maturity is
lower.
5. Duration of a (level) perpetuity is equal to: 1+y/ y
Duration and Convexity - Answers P(y) is convex.
Use second derivative for better approximation.
(Change in P / P) = -D* * change in y + 1/2*convexity*(change in y)^2
Convexity Formula - Answers = 1/P * d2P/dy^2
Balance Sheet Exposure to Interest Rate Risk - Answers Pension funds have liabilities, the PV of future
pensions. Changes in IR affect value. Fund movement in assets to hedge the movement in liabilities.
Management of Interest Rate Risk: Cash Flow Matching and Dedication - Answers Consider pension fund
that needs to pay $100 million in benefits. Can invest in portfolio of zero coupon bonds. (Dedication
Strategy)
Immunise portfolio to IR movement. Cash inflows and obligations offset each other.
Not used. Too many bonds, maybe mispriced, difficult to find bonds match long-term maturities.
Management of Interest Rate Risk: Duration Matching - Answers Invest in portfolio of bonds with
duration equal to duration of liabilities, and with same PV.
Value of assets affected by IR movements same way as liabilities.
Assets = Liabilities, can always pay outflows.
Rules to obtain immunisation from Interest Rate Risk - Answers 1. Value of Bond portfolio = Value of
Liabilities
2. Duration of Assets = Duration of Liabilities
