fbpixel 101 concepts level II | IFT World - Part 7

Category: Essential Concepts for Level II

Essential Concept 61: Valuation Discounts and Premiums for Private Companies

Two factors that affect the valuation of private companies are issues related to control and marketability. When valuing the total equity of a private company, a control premium is added if publicly traded companies are used as the basis for pricing multiple. Discounts for lack of control are used to convert a controlling interest value into a non-controlling equity interest value. The formula for a discount for lack of control is given by:   A discount for lack of marketability (DLOM) is an amount or percentage deducted from the value of an ownership interest to reflect the relative absence of… Read More

101 concepts level II

Essential Concept 62: Forward Pricing and Forward Rate Models

Forward pricing model: It is expressed as:   If T* is 1 and T is 2, the present value of $1 to be received 3 years from today, P(3), is given by P(3) = P(1)F(1, 2). Forward rate model: If we express the forward pricing model in terms of rates, we get the forward rate model.   If T* is 1 and T is 2, then (1 + r(3))3 = (1 + r(1))1(1 + f(1,2))2 Two interpretations of forward rates: Suppose f(1,2), the rate agreed on today for a two-year loan to be made one year from today, is 12%…. Read More

101 concepts level II

Essential Concept 63: Riding the Yield Curve or Rolling Down the Yield Curve

Active bond portfolio managers can outperform the bond market’s return by correctly anticipating changes in interest rates relative to the projected evolution of spot rates. When a yield curve is upward sloping, the forward curve is always above the current spot curve. If a trader does not believe that the yield curve will change its level and shape over an investment horizon, he will buy bonds with a maturity longer than the investment horizon. This strategy is called riding the yield curve or rolling down the yield curve. If the view is correct, the trader’s total return will be greater… Read More

101 concepts level II

Essential Concept 64: Traditional Term Structure Theories

Unbiased expectations (Pure expectations theory): It states that the forward rate is an unbiased predictor of the future spot rate. The implication is that bonds of any maturities are perfect substitutes for each other. For example, buying a bond with a maturity of five years and holding it for three years has the same expected return as buying a three-year bond or buying a series of three one-year bonds. The major limitation of this theory is that it simplistically assumes that investors are risk neutral. Local expectations: This theory is more rigorous than the unbiased expectations theory. Rather than assuming… Read More

101 concepts level II

Essential Concept 65: Pricing a Bond using a Binomial Tree

To find the value of the bond at a particular node, we use the backward induction valuation methodology. Backward Induction: Start at maturity, fill in those values, and work back from right to left to find the bond’s value at the desired node. Refer to the following figure.   The value of the bond is given by the following equation:

101 concepts level II

Essential Concept 66: Confirming the Arbitrage-Free Value of a Bond

To value an option free bond, we can either use the sport rates or a binomial tree. Since both the methods are arbitrage free, the two values should be the same. Consider an option-free bond with four years remaining to maturity, a coupon rate of 2%, and a par value of $100. Assume spot rates are as shown in Exhibit 3. Maturity (Years) One-Year Spot Rate 1 1.000% 2 1.201% 3 1.251% 4 1.404% 5 1.819%   Then the bond value can be calculated as:   Next consider a binomial interest rate tree calibrated to the same spot curve (Exhibit… Read More

101 concepts level II

Essential Concept 67: Relationships between the Values of a Callable or Putable Bond, Straight Bond, and Embedded Option

An embedded option represents a right that can be exercised by the issuer, by the bondholder, or automatically depending on the course of interest rates. Embedded options can be: Simple: call options, put options etc. Complex: estate put, sinking fund bonds etc. A call option decreases the value of a bond to an investor. Therefore, Value of callable bond = Value of straight bond – Value of issuer call option Value of issuer call option = Value of straight bond – Value of callable bond A put option increases the value of a bond to an investor. Therefore, Value of… Read More

101 concepts level II

Essential Concept 68: Duration

Effective duration indicates the sensitivity of a bond’s price to a 100-bps parallel shift of the benchmark yield curve in particular, the government par curve; assuming no change in the bond’s credit spread.   The flowing procedure is used to apply this formula in practice. Given a price (PV0), calculate the implied OAS to the benchmark yield curve at appropriate interest rate volatility. Shift the benchmark yield curve down, generate a new interest rate tree, and then revalue the bond using the OAS calculated in Step 1. This value is PV–. Shift the benchmark yield curve up by the same… Read More

101 concepts level II

Essential Concept 69: Components of a Convertible Bond’s Value

There are a number of investment metrics and ratios that help analyze and value convertible bonds. The conversion value indicates the value of the bond if it is converted at the market price of the shares. The minimum value of a convertible bond is the greater of The conversion value and The value of the underlying option-free bond The market conversion premium represents the price investors effectively pay for the underlying shares if they buy the convertible bond and then convert it into shares. Scaled by the market price of the shares, it represents the premium payable when buying the… Read More

101 concepts level II

Essential Concept 70: Structural Versus Reduced-Form Models

Structural Models Reduced-Form Models What is it? Predict why a default may occur. Based on insights from option pricing theory. The values for debt and equity at time T can be expressed as: D(T) + E(T) = A(T) E(T) = Max[A(T) – K,0] D(T) = A(T) – Max[A(T) – K,0] Probability of default is endogenous to the model. Predict when a default may occur (default time). Statistical methods are used. Default intensity (probability of default over the next period) is estimated using regression analysis on company-specific and macro-economic variables. Default is an exogenous variable that occurs randomly. Assumptions Assets are… Read More

101 concepts level II