Notes - Pricing Money

October 9, 2024

Money Markets

Real money, also known as final money, is money on account at the central bank or physical cash. Other forms of money are merely promises to pay. For example, a check is not money but an instruction for one bank to pay another. Both banks will settle the transaction using their accounts at the central bank, thus completing the transaction using true money.

Inter-bank deposit markets (money markets) are a consequence of the payment system because banks seek a return on customer deposits by lending to other customers or banks. This lending occurs at an agreed interest rate and maturity, typically ranging from overnight to 6 months. For instance, a screen for Swiss-franc deposits might show that a bank bids for (borrows) 3-month funds at 3.30% and offers (lends) them at 3.45%. The 0.15% difference is the bid-offer spread, the bank's profit for making the market. The choice of maturity for borrowing implicitly expresses an opinion on future short-term interest rates. If a company believes interest rates will rise, it might borrow for a longer term at a fixed rate; if it believes rates will fall, it might borrow short-term and roll over the debt at lower rates.

Central banks have significant control over short-term interest rates through their money market operations because commercial banks need to borrow from the central bank to cover overdrafts in their accounts. The rate at which the central bank lends is the official interest rate that is widely reported. Most central banks lend against collateral in repurchase agreements (repos) rather than unsecured lending.

The London money market is very active because it is open for much of the day, bridging time zones in Asia, Europe, and America. The market is most active in major currencies like the US dollar (USD), the euro (EUR), the Japanese yen (JPY), the British pound (GBP), the Swiss franc (CHF), the Canadian dollar (CAD), and the Australian dollar (AUD).

Government Bonds

A bond is a tradable promise to pay a series of cash flows, including interest coupons and the principal at maturity. The simplest type of government debt, Treasury bills (T-bills), pay only the principal at maturity, with no coupons. A bond's price is inversely related to its yield, the effective interest rate. A lower price means a higher yield and a higher price means a lower yield.

Repurchase agreements (repos) are used in the bond market by dealers who have sold a bond but do not own it to borrow that bond from a third party by lending cash. The repo rate, or the interest rate paid on the cash, reflects the demand for that specific bond. A bond in high demand will have a lower repo rate and is said to be "tight" or "special". Most government bonds will trade at the same repo rate, called general collateral (GC).

Stripping allows investors to exchange some government bonds for their individual cash flows, which can be traded separately as zero-coupon bonds.

Non-government bonds, unlike government bonds issued in the domestic currency, carry the risk of default. Investors demand a higher yield to compensate for this credit risk, and rating agencies like Moody's, S&P, and Fitch assess the creditworthiness of issuers.

Futures

Futures contracts eliminate counterparty credit risk by using a clearing house that acts as a central counterparty, guaranteeing the contract. Each futures contract has a detailed specification, including the underlying asset, delivery date, and mechanism, ensuring standardization and eliminating ambiguity. For example, the COMEX gold contract specifies the amount, purity, form, and delivery location of the gold.

Futures markets use margin requirements to protect against default. Initial margin is paid upfront to cover potential losses, and variation margin is paid or received daily based on the contract's value changes. For example, in the COMEX gold contract, the initial margin might be $1,350, and if the price of gold increases, the long will receive variation margin equal to the profit.

Futures contracts can be physically delivered or cash settled. Physical delivery involves transferring the underlying asset, while cash settlement involves paying or receiving the price difference between the contract price and the final settlement price at expiry. For instance, the Brent crude oil futures contract is cash settled because delivering physical oil would be inconvenient.

Arbitrage keeps spot and futures prices in line. Any significant difference in prices creates an opportunity for arbitrageurs to exploit the discrepancy, driving the prices back to equilibrium. Interest-rate futures are traded against bonds, and the difference between the futures price and the bond price is the TED spread.

Swaps

Swaps enable the exchange of fixed-rate for floating-rate debt, allowing market participants to manage interest rate risk by converting between fixed and floating interest payments.

Credit risk in swaps is lower than in loans because only the net interest payments are exchanged. For example, if a company receives 6% fixed on a swap and pays a floating rate that is currently 5%, it will only pay 1% of the notional to the counterparty. However, there is still credit exposure, which can be mitigated by using strategies such as collateralization, break clauses, recouponing, and clearing houses.

Basis swaps are used to exchange floating-rate payments in different currencies, allowing for the conversion of assets or liabilities between currencies. For instance, a basis swap might involve one party depositing dollars and receiving USD Libor, while the other deposits sterling and receives GBP Libor plus a spread, which is the price of the swap.

Options

Options give the holder the right but not the obligation to buy (call option) or sell (put option) an underlying asset at a specified price (strike price) on or before a certain date (expiration date). This allows market participants to limit potential losses while retaining potential gains. For example, a gold miner who wants to protect against falling gold prices but participate in potential price increases can buy a put option with a strike price at or below their production cost.

The price of an option, also known as the premium, is influenced by several factors, including the current forward price of the underlying asset, the volatility of the forward price, and prevailing interest rates. A put option becomes more valuable as the forward price decreases, the volatility of the forward price increases, and interest rates decrease.

Implied volatility, derived from the option price, is the break-even amount of volatility in the price of the underlying asset required to justify the option's price. A higher implied volatility typically leads to a higher option price. For instance, if a gold future is trading at $250 and the implied volatility of a 1-year put option is 17%, the market expects a price swing of roughly ±$42.50 over the next year.

Foreign Exchange

Foreign exchange (FX) markets facilitate international trade and investment by enabling businesses and investors to convert currencies, allowing for cross-border transactions. When a US company wants to purchase goods from a Japanese supplier, it needs to exchange USD for JPY, and the FX market provides the platform for this exchange.

Forward FX contracts enable participants to lock in exchange rates for future dates, mitigating the risk of adverse exchange rate movements.

CLS helps reduce settlement risk in FX transactions by acting as a clearing house, netting payments, and staggering settlement in tranches. This system mitigates the risk of one party defaulting after receiving payment but before delivering the other currency, known as Herstatt risk.

Players

Governments issue bonds, primarily in their domestic currency, to borrow money. They typically utilize auctions to sell their debt and are not very price-sensitive in their issuance.

Pension funds are major long-term investors in fixed-income markets seeking stable, long-term returns to match their liabilities. They often track bond indices, impacting the demand for the bonds included in those indices.

Insurers invest in bonds to hedge their annuity obligations and manage risk associated with their insurance policies. For example, a life insurance company might purchase long-dated bonds to match the cash flows of a life annuity it has sold.

Mutual funds offer a way for individuals to invest in a diversified portfolio of assets, including bonds, based on a predetermined investment strategy.

Hedge funds utilize leverage to take on higher levels of risk aiming for higher returns. Their trading strategies can vary widely, including "macro" trades based on global economic trends and "micro" trades focusing on relative value within an asset class.

Commercial banks raise capital by issuing debt, often in complex forms due to the interaction of bank regulations, tax laws, and investor preferences. One example is the step-up perpetual, which offers a lower coupon initially but steps up significantly if not called after a certain period, appealing to both regulators and investors.

Central banks are active in the domestic money market and manage foreign exchange reserves, primarily investing in short-dated, low-risk assets, mostly in US dollars.

Exchange Traded Funds (ETFs) offer a low-cost and accessible way for individuals to invest in a basket of assets, including stocks and bonds. However, commodity ETFs that track futures can be risky due to the effects of contango and backwardation.

People

Proprietary traders use their employer's capital to profit from market speculation. They are subject to risk limits, but successful proprietary traders can earn significant profits. Effective proprietary traders must remain disciplined, readily adjusting positions based on market movements and avoiding emotional attachment to trades.

Market makers provide liquidity to clients by quoting bid and offer prices for various instruments. They aim to profit from the bid-offer spread while hedging their risk. Market makers require a deep understanding of market dynamics and maintain careful control over their positions.

Salespeople connect clients with the bank's services, including trading, research, and market insights. They act as a conduit between clients and the trading desk, facilitating trades and providing valuable market information.

Researchers provide information and analysis to support traders, salespeople, and clients.

Back and middle office staff are responsible for trade processing and settlement, ensuring the smooth execution and completion of trades.

Investment bankers provide confidential advice to clients on mergers, acquisitions, and other financial matters, working behind a "Chinese wall" to maintain confidentiality.

Price Action

Price movements are driven by buyers and sellers reacting to news and market conditions. The urgency and desperation of buyers or sellers, reflected in their order sizes and prices, can have a significant impact on price action. If a large buyer needs to buy a significant amount of a particular asset quickly, they may drive the price up. Conversely, a large, urgent seller can push prices down. Leverage can exacerbate price movements as participants may be forced to close losing positions, potentially leading to a cascade effect. A leveraged short position that experiences a sudden price increase might need to buy back the asset at a loss, pushing the price even higher.

Fixed-income markets are highly sensitive to central bank policy rates, as these rates influence borrowing costs for governments and corporations. Changes in interest rate expectations, inflation data, and economic indicators can all impact bond prices. For instance, if inflation rises unexpectedly, the market may anticipate that the central bank will raise interest rates, causing bond prices to fall.

Zero-coupon curves are flatter than forward-rate curves, which are in turn flatter than par curves.

Swaps Revisited

Swaps, while having lower credit risk than loans, are not risk-free. Banks employ various strategies to mitigate this risk, including collateralization, break clauses, recouponing, and using clearing houses like SwapClear.

Basis swaps allow for the conversion of floating-rate payments between different currencies. This enables companies to manage their exposure to foreign exchange risk by effectively exchanging floating-rate debt in one currency for floating-rate debt in another. Cross-currency basis swaps can be structured with a constant notional amount or a variable notional amount. Constant notional swaps maintain the same notional in both currencies, while variable notional swaps adjust the notional on the dollar leg to reflect exchange rate fluctuations.

Non-government Issuance

Investment banks play a crucial role in assisting non-government entities in issuing debt. They provide advice, structure the issuance, and market the bonds to investors. For example, if a company wants to issue a bond, an investment bank will advise on the appropriate size, maturity, and coupon rate for the bond, considering market conditions and investor demand.

Book-building is the process of soliciting orders from investors before pricing a bond. This process helps gauge investor interest and determine the optimal price and yield for the new issue.

Syndicates, led by a book-runner, manage the bond issuance process. They allocate bonds to investors and provide market-making support after issuance. The syndicate structure can be complex, involving co-leads and co-managers with varying levels of responsibility.

Corporate debt issuances are subject to legal and regulatory requirements, including selling restrictions, prospectus disclosures, and clauses related to credit protection and force majeure.

Yield, Duration, Repo, and Forward Bond Prices

Yields can be quoted with different compounding frequencies, and it is crucial to convert yields to a common basis for comparison.

Duration and DV01 measure a bond's price sensitivity to changes in yields. Macaulay duration is the weighted average time to receive a bond's cash flows, while modified duration measures the percentage change in a bond's price for a given change in yield. For instance, a bond with a modified duration of 7 will experience a 7% price change for a 1% change in yield.

Barbell trades, involving buying or selling bonds at both ends of the maturity spectrum, are often constructed to be duration-neutral and cash-neutral. This strategy aims to minimize the impact of parallel shifts in the yield curve while potentially profiting from changes in the curve's steepness.

Carry and slide measure the expected return from holding a bond under different yield change scenarios. Carry includes the cost of funding, while slide only considers the change in price due to the passage of time and yield curve movements.

Bond Futures

Bond futures contracts are more complex than futures on other assets due to the deliverable basket of bonds and the use of conversion factors to adjust for differences in coupon rates. This complexity arises from the need to allow for delivery of a range of bonds with varying maturities and coupon rates, while ensuring a fair and transparent settlement process.

The short position in a bond futures contract will choose to deliver the cheapest-to-deliver (CTD) bond. This bond is determined based on factors such as yield levels, the shape of the yield curve, and repo rates, and can change over time.

The basis net of carry (BNOC) for a bond represents the value of the delivery option in the futures contract. Calculating this value can be complex and requires considering factors such as the forward prices of the deliverable bonds, repo rates, and the price of the futures contract.

Basic Fixed-Income Arithmetic

Understanding market conventions in fixed-income trading is crucial for accurate pricing and risk management. These conventions may not always be logical but are essential for consistent and transparent trading practices.

Calculating a bond's duration is essential for managing interest rate risk, allowing traders to understand how a change in interest rates will impact their bond portfolio's value.

Forward yield calculations help assess the potential profitability of trades over a specific horizon by considering the carry, which is the profit or loss from holding a bond over time assuming unchanged yields.