Interest Rate Sensitivity
Topic III – Duration
Interest Rate Sensitivity Price Changes: 1. Bond prices and yields are inversely related: as yields increase bonds prices fall, as yields decrease bond prices increase 2. Decreases in yields have larger impacts on price than increases in yields of equal magnitude [Convex Price Curve] Maturity: 3. Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of short-term bonds • A change in the interest rate will be applied to more-distant cash flows in longer-term bonds 4. Sensitivity of bond prices increases to changes in yields, yet at a decreasing rate as maturity increases Coupon Rates: 5. Prices of low-coupon bonds are more sensitive to changes in interest rates than prices of high-coupon bonds 6. The higher the yield to maturity of a bond, the less sensitive it is to changes in yields Duration – given a 1% relative change in the yield ( change in yield [∂] divided by the level of yield [1 + y] ) how much is the relative change in the value (∂P/P, return) Measure of the sensitivity of price changes to yield / interest changes Measure of the average maturity of the bond’s promised CF’s
Duration (Economic Interpretation) – interest risk measure: the sensitivity of market value (price) to changes in interest rate Duration (Maturity/Life Measure) – the average life (or economic life) of bond (or a security) Duration (Economic Payback Period) – how long on average does it take to get back the cost of your investment, in present value terms
Maturity: Duration INCREASES as Maturity INCREASES, but at a DECREASING rate Duration is the weighted-average time to receive CF’s – as t (maturity) increases, the weight given to CF’s at larger maturities decreases as they are discounted more heavily
Coupon Rate: Duration INCREASES as Coupon Rates DECREASE Duration is the weighted-average time to receive CF’s – the larger C, the higher weights put on those t before maturity, relative to the maturity T, making duration occur faster A higher fraction of the total value of the bond is tied up in the (earlier) coupon payments whose values are relatively insensitive to yields rather than the (later and more yield-sensitive) repayment of par value
Topic VI – Option Strategies Derivatives – financial instruments whose value is determined by some observable variable (usually other securities) 1.
Derivatives depends on a financial asset – that asset is denoted to as the underlying asset (S)
2.
Derivatives live for a pre-defined period – denoted as the time till maturity (T) • Many derivatives have all their cash flow consequences at time (T) • Current time-point is denoted as (t)
Options – derivatives that give the holder the right, but not the obligation, to trade the underlying asset
Price at which the asset can be bought/sold under the option is called the strike price or exercise price (X)
If an option is used to buy/sell the underlying asset, it’s said to be exercised
Intrinsic Value – the value an option would have if exercised today (S0 – X) Call Option – gives the holder the right to buy an asset for a specified price, on or before some specified expiry date St > X [BUY at Discount] Current market price of the Underlying Asset > Exercise Price, option allows the holder to buy at a discount Intrinsic Value = Size of the Discount, St – X St < X [No Buy] Option holder would rather buy the underlying asset at the current market price and will ignore the option Intrinsic Value = 0, max(0, St – X) Put Option – gives the holder the right to sell an asset for a specified price, on or before some specified expiry date St < X [SELL at Premium] Current market price of the Underlying Asset < Exercise Price, option allows the holder to buy at a discount Intrinsic Value = Size of the Price Increase, X – St St > X [No Sell] Option holder would rather sell the underlying asset at the current market price and will ignore the option Intrinsic Value = 0, max(0, X – St) Moneyness: Options can be raised as deep in the money / deep out of the money to emphasise the distance of X and St In the Money (+ve Intrinsic Value) Call Options: St > X Put Options: St < X
At the Money (X = St)
Time Value – the value rising from the possibility that the price of the underlying asset will change to increase the value of the option (Increase for Call option, Decrease for Put Option) Time Value is ALWAYs +ve until expiration – the value of not having to exercise your option today Probability of an option’s moneyness increasing, increases with: 1. Time to Maturity – the time value of an option increases with the time to maturity 2.
Volatility of the Underlying Asset Price – the time value of an option increases with the underlying volatility
Total Value
=
Intrinsic Value
+
Time Value
Interest Rate Sensitivity Price Changes: 1. Bond prices and yields are inversely related: as yields increase bonds prices fall, as yields decrease bond prices increase 2. Decreases in yields have larger impacts on price than increases in yields of equal magnitude [Convex Price Curve] Maturity: 3. Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of short-term bonds • A change in the interest rate will be applied to more-distant cash flows in longer-term bonds 4. Sensitivity of bond prices increases to changes in yields, yet at a decreasing rate as maturity increases Coupon Rates: 5. Prices of low-coupon bonds are more sensitive to changes in interest rates than prices of high-coupon bonds 6. The higher the yield to maturity of a bond, the less sensitive it is to changes in yields Duration – given a 1% relative change in the yield ( change in yield [∂] divided by the level of yield [1 + y] ) how much is the relative change in the value (∂P/P, return) Measure of the sensitivity of price changes to yield / interest changes Measure of the average maturity of the bond’s promised CF’s
Duration (Economic Interpretation) – interest risk measure: the sensitivity of market value (price) to changes in interest rate Duration (Maturity/Life Measure) – the average life (or economic life) of bond (or a security) Duration (Economic Payback Period) – how long on average does it take to get back the cost of your investment, in present value terms
Maturity: Duration INCREASES as Maturity INCREASES, but at a DECREASING rate Duration is the weighted-average time to receive CF’s – as t (maturity) increases, the weight given to CF’s at larger maturities decreases as they are discounted more heavily
Coupon Rate: Duration INCREASES as Coupon Rates DECREASE Duration is the weighted-average time to receive CF’s – the larger C, the higher weights put on those t before maturity, relative to the maturity T, making duration occur faster A higher fraction of the total value of the bond is tied up in the (earlier) coupon payments whose values are relatively insensitive to yields rather than the (later and more yield-sensitive) repayment of par value
Topic VI – Option Strategies Derivatives – financial instruments whose value is determined by some observable variable (usually other securities) 1.
Derivatives depends on a financial asset – that asset is denoted to as the underlying asset (S)
2.
Derivatives live for a pre-defined period – denoted as the time till maturity (T) • Many derivatives have all their cash flow consequences at time (T) • Current time-point is denoted as (t)
Options – derivatives that give the holder the right, but not the obligation, to trade the underlying asset
Price at which the asset can be bought/sold under the option is called the strike price or exercise price (X)
If an option is used to buy/sell the underlying asset, it’s said to be exercised
Intrinsic Value – the value an option would have if exercised today (S0 – X) Call Option – gives the holder the right to buy an asset for a specified price, on or before some specified expiry date St > X [BUY at Discount] Current market price of the Underlying Asset > Exercise Price, option allows the holder to buy at a discount Intrinsic Value = Size of the Discount, St – X St < X [No Buy] Option holder would rather buy the underlying asset at the current market price and will ignore the option Intrinsic Value = 0, max(0, St – X) Put Option – gives the holder the right to sell an asset for a specified price, on or before some specified expiry date St < X [SELL at Premium] Current market price of the Underlying Asset < Exercise Price, option allows the holder to buy at a discount Intrinsic Value = Size of the Price Increase, X – St St > X [No Sell] Option holder would rather sell the underlying asset at the current market price and will ignore the option Intrinsic Value = 0, max(0, X – St) Moneyness: Options can be raised as deep in the money / deep out of the money to emphasise the distance of X and St In the Money (+ve Intrinsic Value) Call Options: St > X Put Options: St < X
At the Money (X = St)
Time Value – the value rising from the possibility that the price of the underlying asset will change to increase the value of the option (Increase for Call option, Decrease for Put Option) Time Value is ALWAYs +ve until expiration – the value of not having to exercise your option today Probability of an option’s moneyness increasing, increases with: 1. Time to Maturity – the time value of an option increases with the time to maturity 2.
Volatility of the Underlying Asset Price – the time value of an option increases with the underlying volatility
Total Value
=
Intrinsic Value
+
Time Value
