- Information
- AI Chat
Project proposal (2) (1)
Derivatives and Risk Management (Options, Futures and Derivatives)
SVKM's NMIMS
Recommended for you
Preview text
Derivatives - Valuation and Strategies 29. ─ Sachin Saroa NMIMS Global Access - School for Continuing Education (NGASCE) Question No. 3 (a) The questions are based on the trading and Valuation concept of Option
a) What is the rationale behind the implementation of a stop-loss trading rule for the seller or writer of an out-of-the-money call option, and why does this particular strategy tend to offer a suboptimal hedge against potential losses? (5 Marks) The stop-loss trading rule is a crucial risk management strategy used by traders, including those who write or sell options. Let’s delve into the rationale behind it and explore why it’s essential: Risk Control and Loss Limitation: Options, including call options, can be highly volatile and subject to sudden price movements. Stop-loss orders allow traders to define a specific price level at which they will exit a position to limit potential losses. For call option writers, implementing a stop-loss helps prevent significant losses if the underlying asset’s price moves against their position. Leverage and Risk: Leverage is a double-edged sword. While it amplifies potential gains, it also magnifies losses. Option writers use leverage to maximize gains, but this also exposes them to substantial risk. A stop-loss acts as a safety net, ensuring that losses are contained within acceptable limits. Out-of-the-Money Call Options: An out-of-the-money (OTM) call option has a strike price higher than the current market price of the underlying asset. Writers of OTM call options receive a premium upfront but face the risk of having to deliver the asset if the option is exercised. Implementing a stop-loss helps mitigate the risk of substantial losses if the underlying asset’s price rises unexpectedly. Challenges with Stop-Loss for Call Option Writers: Suboptimal Hedge: While stop-losses are effective for managing risk, they may not provide an optimal hedge for call option writers.
b) Could you elucidate the notion of valuation as it pertains to dividend-paying stocks within the context of American call and European call options, with a specific focus on the determination of intrinsic value? (5 Marks) Certainly! Let’s delve into the valuation of dividend-paying stocks within the context of American and European call options, with a focus on intrinsic value. Dividends and Option Pricing: Dividends play a crucial role in determining the prices of options (both call and put) on dividend-paying stocks. When a stock pays dividends, the holders of the underlying shares receive these dividend payments, but the holders of call and put options do not. As a result, the payment of dividends affects the pricing of options. Ex-Dividend Date and Stock Price Drop: The ex-dividend date is the first trading day where an upcoming dividend payment is not included in a stock’s price. On the ex-dividend date, the stock price typically drops by the amount of the dividend. This is because the company is forfeiting that money, making the stock worth less. However, other factors (such as market dynamics) can also impact the stock price on the ex-dividend date. Impact on Call Options: Call options give the holder the right to buy the underlying stock at a specified strike price. Leading up to the ex-dividend date, call options become less expensive because of the expected fall in the stock price due to the dividend payment. Holders of deep-in-the-money American-style call options may choose to exercise them early before the ex-dividend date to capture the dividend owed to the underlying shares. European vs. American Call Options: European call options can only be exercised at expiration, while American call options can be exercised at any time before expiration. The Black-Scholes formula, commonly used for option pricing, is not well- equipped for valuing American options on dividend-paying stocks.
Determining Intrinsic Value: Intrinsic value represents the difference between the current stock price and the strike price of the option. For call options, intrinsic value is calculated as the maximum of (stock price - strike price) or zero. When considering dividends, the stock price used in this calculation should account for the expected dividend payment. In summary, dividends impact option prices, especially call options, and understanding their effect is essential for informed trading decisions. Remember that the Black-Scholes model may not fully capture the complexities of American options on dividend-paying stocks. Question No. 2 (b) “Based on valuations at mid-2023, convertibles’ low equity sensitivity argues for a more “bond-like” return profile in the near term; a rebound in corporate earnings could drive further upside.” Provide a detailed report mentioning the detailed features of convertible bonds along with different terms associated with convertible bonds. Also, explain when a convertible bond exhibits the equity and bond-like characteristics. (10 marks) VALUATION AND ANALYSIS OF CONVERTIBLE BONDS So far, we have discussed bonds for which the exercise of the option is at the discretion of the issuer (callable bond), at the discretion of the bondholder (putable bond), or set through a pre-defined contractual arrangement (capped and floored floaters). What distinguishes a convertible bond from the bonds discussed earlier is that exercising the option results in the change of the security from a bond to a common stock. This section describes defining features of convertible bonds and discusses how to analyze and value these bonds. 6 Defining Features of a Convertible Bond A convertible bond is a hybrid security. In its traditional form, it presents the characteristics of an option-free bond and an embedded conversion option. The conversion option is a call option on the issuer’s common stock, which gives bondholders the right to convert their debt into equity during a predetermined period (known as the conversion period) at a predetermined price (known as the conversion price).
It is more frequent for convertible bonds to include a call option that gives the issuer the right to call the bond during a specified period and at specified times. As discussed earlier, the issuer may exercise the call option and redeem the bond early if interest rates are falling or if its credit rating is revised upward, thus enabling the issuance of debt at a lower cost. The issuer may also believe that its share price will increase significantly in the future because of its performance or because of events that will take place in the economy or in its sector. In this case, the issuer may try to maximize the benefit to its existing shareholders relative to convertible bondholders and call the bond. To offer convertible bondholders protection against early repayment, convertible bonds usually have a lockout period. Subsequently, they can be called but at a premium, which decreases as the maturity of the bond approaches. If a convertible bond is callable, the issuer has an incentive to call the bond when the underlying share price increases above the conversion price in order to avoid paying further coupons. Such an event is called forced conversion because it forces bondholders to convert their bonds into shares. Otherwise, the redemption value that bondholders would receive from the issuer calling the bond would result in a disadvantageous position and a loss compared with conversion. Even if interest rates have not fallen or the issuer’s credit rating has not improved, thus not allowing refinancing at a lower cost, the issuer might still proceed with calling the bond when the underlying share price exceeds the conversion price. Doing so allows the issuer to take advantage of the favorable equity market conditions and force the bondholders to convert their bonds into shares. The forced conversion strengthens the issuer’s capital structure and eliminates the risk that a subsequent correction in equity prices prevents conversion and requires redeeming the convertible bonds at maturity. Analysis of a Convertible Bond There are a number of investment metrics and ratios that help in analyzing and valuing a convertible bond. 6.2 Conversion Value The conversion value or parity value of a convertible bond indicates the value of the bond if it is converted at the market price of the shares.
Conversion value = Underlying share price × Conversion ratio Minimum Value of a Convertible Bond The minimum value of a convertible bond is equal to the greater of ● the conversion value and ● the value of the underlying option-free bond. Theoretically, the value of the straight bond (straight value) can be estimated by using the market value of a non-convertible bond of the issuer with the same characteristics as the convertible bond but without the conversion option. In practice, such a bond rarely exists. Thus, the straight value is found by using the arbitrage- free framework and by discounting the bond’s future cash flows at the appropriate rates. The minimum value of a convertible bond can also be described as a floor value. It is a moving floor, however, because the straight value is not fixed; it changes with fluctuations in interest rates and credit spreads. If interest rates rise, the value of the straight bond falls, making the floor fall. Similarly, if the issuer’s credit spread increases as a result, for example, of a downgrade of its credit rating from investment grade to non-investment grade, the floor value will fall too. 6.2 Market Conversion Price, Market Conversion Premium per Share, and Market Conversion Premium Ratio Many investors do not buy a convertible bond at issuance on the primary market but instead buy such a bond later in its life on the secondary market. The market conversion premium per share allows investors to identify the premium or discount payable when buying the convertible bond rather than the underlying common stock. Although discounts are rare, they can theoretically happen given that the convertible bond and the underlying common stock trade in different markets with different types of market participants. For example, highly volatile share prices may result in the market conversion price being lower than the underlying share price. Market conversion premium per share = Market conversion price - Underlying share price where
All else being equal, the higher the premium over straight value, the less attractive the convertible bond. Despite its use in practice, the premium over straight value is a flawed measure of downside risk because, as mentioned earlier, the straight value is not fixed but rather fluctuates with changes in interest rates and credit spreads. Upside Potential of a Convertible Bond The upside potential of a convertible bond depends primarily on the common stock. prospects of the underlyingThus, convertible bond investors should be familiar with the techniques used to value and analyze common stocks. These techniques are covered in other readings. Valuation of a Convertible Bond Historically, the valuation of convertible bonds has been challenging because these securities combine characteristics of bonds, stocks, and options, thus requiring an understanding of what affects the value of fixed income, equity, and derivatives. The complexity of convertible bonds has also increased over time as a result of market innovations as well as additions to the terms and conditions of these securities. For example, convertible bonds have evolved into contingent convertible bonds and convertible contingent convertible bonds, which are even more complex to value and analyze. Contingent convertible bonds, or “CoCos,” pay a higher coupon than otherwise identical non-convertible bonds, but they are usually deeply subordinated and may be converted into equity or face principal write-downs if regulatory capital ratios are breached. Convertible contingent convertible bonds, or “CoCoCos,” combine a traditional convertible bond and a CoCo. They are convertible at the discretion of the investor, thus offering upside potential if the share price increases, but they are also converted into equity or face principal write-downs in the event of a regulatory capital breach. CoCos and CoCoCos are usually issued by financial institutions, particularly in Europe. The fact that many bond’s prospectuses or offering circulars frequently provide for an independent financial valuer to determine the conversion price (and in essence the value of the convertible bond) under different scenarios is evidence of the complexity associated with valuing convertible bonds. Because of this complexity, convertible bonds in many markets come with selling restrictions. They are typically offered in very high denominations and only to professional or institutional investors. Regulators perceive them as securities that are too risky for retail investors to invest in directly.
As with any fixed-income instrument, convertible bond investors should perform a diligent risk–reward analysis of the issuer, including its ability to service the debt and repay the principal, as well as a review of the bond’s terms of issuance (e., collateral, credit enhancements, covenants, and contingent provisions). In addition, convertible bond investors must analyze the factors that typically affect bond prices, such as interest rate movements. Because most convertible bonds have lighter covenants than otherwise similar non-convertible bonds and are frequently issued as subordinated securities, the valuation and analysis of some convertible bonds can be complex. The investment characteristics of a convertible bond depend on the underlying share price, so convertible bond investors must also analyze factors that may affect the issuer’s common stock, including dividend payments and the issuer’s actions (e., acquisitions or disposals, rights issues). Even if the issuer is performing well, adverse market conditions might depress share prices and prevent conversion. Thus, convertible bond investors must also identify and analyze the exogenous reasons that might ultimately have a negative effect on convertible bonds. Academics and practitioners have developed advanced models to value convertible bonds, but the most commonly used model remains the arbitrage-free framework. A traditional convertible bond can be viewed as a straight bond and a call option on the issuer’s common stock, so Value of convertible bond = Value of straight bond + Value of call option on the issuer’s stock Many convertible bonds include a call option that gives the issuer the right to call the bond during a specified period and at specified times. The value of such bonds is Value of callable convertible bond = Value of straight bond + Value of call option on the issuer’s stock – Value of issuer call option Suppose that the callable convertible bond also includes a put option that gives the bondholder the right to require that the issuer repurchases the bond. The value of such a bond is Value of callable putable convertible bond = Value of straight bond + Value of call option on the issuer’s stock – Value of issuer call option + Value of investor put option
In between the bond and the stock extremes, the convertible bond trades like a hybrid instrument. It is important to note the risk–return characteristics of convertible bonds (1) when the underlying share price is below the conversion price and increases toward it and (2) when the underlying share price is above the conversion price but decreases toward it. In the first case, the call option component increases significantly in value as the underlying share price approaches the conversion price. The return on the convertible bond during such periods increases significantly but at a lower rate than the increase in the underlying share price because the conversion price has not been reached yet. When the share price exceeds the conversion price and goes higher, the change in the convertible bond price converges toward the change in the underlying share price— In the second case (that is, when the underlying share price is above the conversion price but decreases toward it), the relative change in the convertible bond price is less than the change in the underlying share price because the convertible bond has a floor. As mentioned earlier, this floor is the minimum value of the convertible bond, which in this case is equal to the value of the underlying option-free bond. Except for busted convertibles, the most important factor in the valuation of convertible bonds is the underlying share price. However, it is worth mentioning that large movements in interest rates or in credit spreads may significantly affect the value of convertible bonds. For a convertible bond with a fixed coupon, all else being equal, a significant fall in interest rates would result in an increase in its value and price, whereas a significant rise in interest rates would lead in a decrease in its value and price. Similarly, all else being equal, a significant improvement in the issuer’s credit quality would result in an increase in the value and price of its convertible bonds, whereas a deterioration of the issuer’s credit quality would lead to a decrease in the value and price of its convertible bonds. ABC A convertible bond is a financial instrument that combines features of both equity and debt. Let’s delve into the characteristics that make it a hybrid: Bond-Like Characteristics: Fixed Principle: Like traditional bonds, convertible bonds have a fixed principal amount (the face value) that the issuer must repay at maturity.
Fixed Interest Rate: Convertible bonds pay regular interest payments (coupons) to bondholders at predetermined intervals. Fixed Maturity: These bonds have a specific maturity date when the issuer must redeem them. Equity-Like Characteristics: Conversion Option: The unique feature of convertible bonds is their conversion privilege. Bondholders can choose to convert their bonds into a predetermined number of common stock shares of the issuing company. At the Discretion of Bondholder: The conversion typically occurs at specific times during the bond’s life and is usually at the discretion of the bondholder. Opportunity to Own Stock: By converting, bondholders can become shareholders and participate in the company’s equity ownership. In summary, convertible bonds offer investors the stability of fixed income (like bonds) while providing the option to participate in potential stock gains (like equity). They behave like bonds when the underlying stock falls and more like stocks when the underlying stock rises, making them a versatile investment choice. “The key rate duration is considered a superior metric to effective duration” Question 3 (a) A) Explain the shaping risk associated with the bond. Also, explain how the key rate duration is a better measure than effective duration to measure the shaping risk associated with bonds. (5 marks) Certainly! Shaping risk in the context of bonds refers to the sensitivity of a bond’s price to changes in the shape of the yield curve. Let’s break it down: 1. Yield Curve Risk: ○ The yield curve represents the relationship between interest rates (or yields) and the time to maturity of bonds. It can take various shapes, such as upward-sloping (normal), flat, or downward-sloping (inverted).
Remember, shaping risk is essential for bond investors to understand and manage their exposure to yield curve movements1 23. 📈📉 Certainly! Let’s delve into the nuances of key rate duration and how it compares to effective duration in assessing the shaping risk associated with bonds. 1. Key Rate Duration: ○ Definition: Key rate duration measures a bond’s sensitivity to a small change in a benchmark yield curve at a specific spot rate, while keeping all other factors constant. ○ Purpose: Unlike effective duration, which assumes parallel shifts in the yield curve, key rate duration allows for identifying and managing risk associated with non-parallel shifts in the yield curve. ○ Calculation: It quantifies the possible change in bond value resulting from a 100-basis- point (1%) change in yield for a given maturity. ○ Application: Key rate duration is particularly useful for assessing the impact of interest rate changes on bonds with embedded options (such as callable bonds). ○ Example: If the yield curve shifts in a non-parallel manner (e., different rates change at different maturities), key rate duration provides insights into how bond prices will fluctuate at specific points along the curve1. 2. Effective Duration: ○ Definition: Effective duration measures the impact of cash flows on bonds, considering factors like coupon payments and embedded options (e., call or put options). ○ Purpose: It helps investors understand how bond prices will change due to fluctuations in interest rates. ○ Calculation: Effective duration considers the present value of all future cash flows (coupons and principal) and their sensitivity to interest rate changes. ○ Application: Effective duration is commonly used for bonds with embedded options, as it accounts for the timing and magnitude of cash flows. ○ Example: When interest rates change, effective duration reflects the impact on bond prices based on the entire cash flow profile1. 3. Comparison: ○ Risk Assessment: Key rate duration is more suitable for assessing risk when the yield curve moves in a non-parallel manner. It captures the specific sensitivities at different points along the curve.
○ Portfolio Management: Key rate duration allows investors to manage their portfolios by adjusting bond durations strategically. For instance, options traders may use key rate duration hedging to minimize duration risk. ○ Limitations: While effective duration is valuable, it assumes parallel shifts in the yield curve, which may not always hold true. Key rate duration provides a more nuanced view of risk. ○ Trade-Off: Key rate duration may involve some hedging costs, but it offers a better understanding of bond price movements in complex scenarios1 23. In summary, key rate duration provides a finer-grained analysis of bond price sensitivity, especially in situations where yield curve movements are not uniform. Effective duration remains valuable but may overlook specific risks associated with non-parallel shifts in the curve. As investors, understanding both metrics helps us make informed decisions in bond markets. Question 3 (b) B) Enlist the properties of key rate duration associated with callable and putable bonds. Callable Bonds: The effective duration of a callable bond cannot be greater than that of a straight bond. As interest rates rise above the coupon rate, the call option becomes out of the money. Therefore, straight and callable bonds will have the same effective durations. When interest rates fall, the call option moves into the money, and the bond is most likely called. Thus, the call option reduces the effective duration of the callable bond relative to that of a straight bond. Putable Bonds: The effective duration of a putable bond cannot exceed that of a straight bond. When interest rates fall below the bond’s coupon rate, the put option will be out of the money. In this case, the effective duration of a putable bond will be identical to that of a straight bond. When interest rates rise, the put option moves into the money. The bond is more likely to be put, meaning that its downward potential is limited.
Project proposal (2) (1)
Course: Derivatives and Risk Management (Options, Futures and Derivatives)
University: SVKM's NMIMS
- Discover more from:
