The literature labels crises by different expressions. One distinction is between banking crises and currency crises. The origin of a banking crisis is severe balance sheet weaknesses in one or several banks, which are big enough to affect the whole banking sector. The currency crisis is the collapse of the exchange rate system following a speculative attack on the domestic currency.
Generally, the term ‘financial crisis’ is used to encompass both. If you dig a little deeper, it is likely to find titles such as balance of payments and capital account crises -both point to extreme difficulties in financing the current account deficit, which causes a sharp depreciation and spills over the rest of the economy overnight. In some theoretical models that try to explain crises, distinguishing banking and currency crises may not be possible. In the rest of this chapter, we focus on financial
crises, remembering that a balance of payment or currency crisis can immediately turn into a financial crisis. Mor
Doğru cevap: C) Financial crises encompass both banking and currency crises, with the term "financial crisis" being used to refer to either.

Whenever there is a balance sheet flaw, there is a concern. It can occur in the public sector. For
example, the budget deficit can be extremely high in a row of years, leading to a high public debt-toGDP ratio that elevates the sovereign risk premium and interest rates. Nonfinancial corporations may have high foreign currency exposure; a large gap between foreign currency-denominated liabilities and assets. Or, due to a prolonged economic recession, they may face severe concerns in honoring their debts. By a burst of a crisis because of a triggering factor, problems of the nonfinancial firms can become issues of the financial sector overnight. Financial institutions may suffer from inadequate capital levels, low capital-to-assets ratios, currency, and maturity mismatches. In the beginning, balance sheet weaknesses may be barely noticeable. However, they accumulate over time unless contained. A significant shock -external, as in the global financial crisis that first started in the US, or a domestic on
Doğru cevap: C) Balance sheet weaknesses accumulate over time and can be triggered by significant shocks, whether external or domestic, leading to full-scale financial crises.

During a crisis, banks become more cautious and reluctant to extend new loans, exacerbating nonfinancial firm problems. Layoffs begin, and employment declines. Increased risk, elevated interest rates, and rising unemployment decrease aggregate demand. The currency depreciation increases the debt burden of households and firms with foreign currency-denominated debt,
further reducing aggregate demand and increasing unemployment. Economic activity stagnates and, in most cases, contracts.
Doğru cevap: D) Financial crises often result in banks becoming more cautious and reluctant to extend new loans, leading to layoffs, declining employment, decreased aggregate demand, and economic stagnation or contraction.

On the eve of a crisis, risk aversion increases. In this environment, we generally observe a rise in risk premium and interest rates and a pressure of depreciation on the domestic currency. With the crisis burst, the domestic currency depreciates in a flexible exchange rate regime. Suppose it is a fixed exchange rate regime or a variant. In that case, authorities devalue the domestic currency and either try to stick to the previous exchange rate regime, albeit at a higher exchange rate, or shift to a flexible one. Simultaneously, risk appetite for the financial assets of that country declines sharply, and interest rates jump. No matter how the crisis is shaped, it quickly spreads to nonfinancial and financial corporations.
Doğru cevap: C) Risk aversion increases on the eve of a crisis, resulting in a rise in risk premium and interest rates, and pressure for depreciation on the domestic currency.

In a contracting economy, unemployment increases. In the crises analyzed by Reinhart and Rogoff, the unemployment rate increased by sevenpercentage points on average. For example, the average unemployment rate in advanced countries in 2022 was 4.7 percent. Therefore, it is immediately evident that the seven-percentage points increase is exceptionally high. Another point to be emphasized is that while the period of economic contraction lasted 1.9 years on average in these crises, the rise in unemployment spread over 4.8 years." Please make this question at moderate difficulty.
Doğru cevap: D) On average, economic crises lead to a significant increase in unemployment rates by approximately 7 percentage points, spreading over a period of 4.8 years.

The rise in the unemployment rate during the global financial crisis was also sizeable. It elevated from 5.5 percent to 8.4 percent in 2010 in advanced economies. The US -the epicenter of the global financial crisis- witnessed a five-percentage point increase in the unemployment rate during the same period: 9.6 percent in 2010 compared to 4.6 percent in 2007.
Doğru cevap: E) 5.0 percentage points

Short-term maturity mismatch arising from the positive gap between short-term liabilities and assets can lead a bank to face liquidity problems, especially in financial distress. From this perspective, ‘shortterm’ refers to one-month or shorter maturities.
Doğru cevap: E) Maturities lasting less than one month

A similar condition can happen to banks holding large amounts of government bonds. We witnessed an example of this in the European crisis that intensified in 2011. Market participants became extremely reluctant to hold financial assets issued by the governments of Greece, then Portugal, Ireland, Spain, and Italy. The reason was the widespread belief that these countries could not repay their debts. Those who held the bonds of these states quickly anticipated to get rid of them. The supply of bonds in the secondary market increased, and their prices fell (sovereign interest rates rose). Eventually, Greece’s sovereign debt market collapsed. Figure 2.6 depicts Greece’s sovereign risk premium -measured by Credit Default Swaps (CDS)- during that period. CDS can be taken as insurance that the person who purchases the riskybond buys to hedge the risk. The higher the risk is, the higher the insurance premium one will pay. The market value of the banks’ assets that still held these bonds on their balance sheets thu
Doğru cevap: D) Due to the widespread belief that these governments would not be able to repay their debts

The balance sheet of each financial institution must be sound. However, the extent to which these institutions are interconnected and their links with financial institutions abroad are also crucial. Liquidity shortages pose a danger to the soundness of a financial system. Another critical issue is the procyclical credit extension behavior of banks.
Doğru cevap: A) Interconnectedness of financial institutions and liquidity shortages

Systemic risk can also evolve from the relationship between financial institutions and the real economy. GDP can remain above or below its trend for a considerable time. Consider a period when the growth rate is above trend. Assume that such a period lasts for a while -say three years- and creates a prosperous economic atmosphere. ‘Things will always be like this’ may become the consensus view. If this happens, risk appetite increases. In this environment, both credit demand and credit supply escalate. Banks may increase their foreign debts for more funding. This process poses two risks: First, rapid credit growth is not sound because credit quality is declining. Second, the connections among the banks I mentioned above become extremely strong. When, for whatever reason, a period of rapid growth ends and a period of sluggish growth begins, especially if this period of slow growth tends to turn into an economic contraction, the borrowers have difficulty repaying the loans. The banking sector starts to strug
Doğru cevap: D) Declining credit quality and strengthened connections among banks

The balance sheet of each financial institution must be sound. Concerns such as maturity mismatch, nonperforming assets, insufficient capital, high leverage, currency mismatch, and liquidity shortages could lead the financial system and, eventually, a country’s economy to a crisis.

The currency crisis is the collapse of the exchange rate system following a speculative attack on the domestic currency.

During a crisis, banks become more cautious and reluctant to extend new loans, exacerbating nonfinancial firm problems. Layoffs begin, and employment declines. Increased risk, elevated interest rates, and rising unemployment decrease aggregate demand. The currency depreciation increases the debt burden of households and f irms with foreign currency-denominated debt, further reducing aggregate demand and increasing unemployment. Economic activity stagnates and, in most cases, contracts.

There are various bases of financial instability. The most important ones are the following: the difference between foreign currency-denominated liabilities and foreign currency-denominated assets (currency mismatches), maturity mismatches, nonperforming assets, capital inadequacy, liquidity shortages, and systemic risk.

The net stable funding ratio is the ratio of available stable funding to the required stable funding.

The leverage ratio is a bank’s capital measure divided by its exposure measure.

Macroprudential policies aim at minimizing systemic risks.

Systemic risk can also evolve from the relationship between financial institutions and the real economy. GDP can remain above or below its trend for a considerable time. Consider a period when the growth rate is above trend. Assume that such a period lasts for a while -say three years- and creates a prosperous economic atmosphere. ‘Things will always be like this’ may become the consensus view. If this happens, risk appetite increases. In this environment, both credit demand and credit supply escalate. Banks may increase their foreign debts for more funding. This process poses two risks: First, rapid credit growth is not sound because credit quality is declining. Second, the connections among the banks I mentioned above become extremely strong. When, for whatever reason, a period of rapid growth ends and a period of sluggish growth begins, especially if this period of slow growth tends to turn into an economic contraction, the borrowers have difficulty repaying the loans. The banking sector starts to struggle with problems, a systemic risk.

Short-term maturity mismatch arising from the positive gap between short-term liabilities and assets can lead a bank to face liquidity problems, especially in financial distress. From this perspective, ‘short term’ refers to one-month or shorter maturities.

On the eve of a crisis, risk aversion increases. In this environment, we generally observe a rise in risk premium and interest rates and a pressure of depreciation on the domestic currency.

A financial return is the gain or loss generated by an investment over a specific period, expressed as a percentage of the initial investment amount. It represents the change in the value of an investment, which may result from capital appreciation, dividends, interest, or other income sources. Financial return is a key metric investors use to evaluate the performance of investments and compare different investment options, as it provides a measure of the rewards obtained from an investment relative to its initial cost. In essence, a financial return quantifies the profitability of an investment and helps investors assess the effectiveness of their investment decisions. A simple percentage return calculation is straightforward. More importantly, we can present the main reasons why financial return calculations are critical.
The correct answer is "B) The change in the value of an investment over a specific period."

First, investors use financial returns to evaluate the performance of different investment options, such as stocks, bonds, or real estate. By comparing returns, they can make informed decisions about where to allocate their resources to maximize their profits. As a second point, financial returns assist investors in understanding the level of risk associated with different investments. Higher returns often come with higher risks, so assessing the balance between risk and reward is crucial for successful investing. Finally, financial returns allow investors and managers to measure a portfolio’s performance or a specific investment over time. This can help them determine whether their investment strategies are effective or need adjustments.
Doğru cevap
D) Financial returns enable investors to evaluate the performance of different investment options and assess risk-reward balance.

The investment horizon is crucial in finance, affecting risk and return calculations. Investors often keep their investments for more than one period, and as the investment horizon increases, the expected returns and actual outcomes tend to differ.
Retirement plans usually have a longer investment horizon than other types of investments. Therefore, it is crucial to present long-term return calculations for these plans. Regulatory authorities also understand the significance of investment horizons and differentiate their regulations based on the type of investment. Banks, for example, might consider a shorter investment horizon if they frequently buy and sell securities. Alternatively, they may invest longer, enabling them to assess their risk and return profiles over an extended duration.
Doğru cevap
D) Banks may adjust their investment horizons based on trading frequency, affecting risk and return assessments.

There are often situations where our investment horizon exceeds one or two years. Therefore, extending the formula mentioned earlier is necessary to cover longer periods. The k-period return formula is an extension of the previous 2-year return formula. It allows us to calculate the return of an investment held by an investor for any period ranging from 1 to k.
Doğru cevap:
D) The k-period return formula extends the calculation of returns beyond two years, catering to longer investment horizons.

Logarithmic return is a financial return measure used to determine the percentage change in an asset’s price over a specific period using logarithmic functions. This return formula is preferred since it accounts for the compounding effect of investment returns.
Doğru cevap:
C) Logarithmic return accounts for the compounding effect of investment returns and is calculated using exponential functions.

Typically, when nominal asset values are small, linear and logarithmic returns tend to be similar. However, as the nominal asset values increase, these two measures start to diverge from each other. One of the benefits of using logarithmic returns is their simplicity in the multi-period return formula.
Doğru cevap
D) Logarithmic returns offer simplicity in the multi-period return formula, particularly as nominal asset values increase.

In finance, short-term Treasury interest rates are considered risk-free or default-free because governments are assumed to be able to back their debts without defaulting. As a result, financial returns are often analyzed using this benchmark. The difference between the returns on risky stocks and Treasury yields is the equity risk premium or excess return. To calculate the excess return, one subtracts the risk-free rate (represented by the Treasury interest rate) at time t, denoted by rF,t , from the stock’s return.
Doğru cevap: B) The excess return is calculated by subtracting the risk-free rate from the stock's return.

The excess return, the difference between the risky and risk-free returns, is essential when evaluating investment performance. Treasury yields typically represent the risk-free return and serve as an opportunity cost for holding a risky asset. When Treasury yields are high, most investors may be satisfied with these risk-free yields. Therefore, when treasury yields are high, demand for risky assets is lower. Stock market instruments are usually less prevalent in these periods. Since these yields are assumed to be risk-free, an investor looking for a better yield needs to take a higher risk. Consequently, stock markets and risky assets do not perform well during high interest rate periods. When treasury yields are low, the demand for risky assets such as stocks increases. It is generally hard to generalize, but low interest environment increases demand for stock markets.
Doğru cevap
B) Low Treasury yields generally result in decreased demand for risky assets as investors prefer the safety of government bonds.

Statistical moments like the mean and variance play a crucial role in analyzing the features of a distribution. These moments provide essential information about the central tendency and dispersion of the distribution, which are important considerations in modeling uncertainty. The selection of a distribution for modeling uncertainty is based on the desired characteristics of the distribution and is often determined by the moments. Once a distribution is chosen, its parameters can be estimated using the moments, allowing analysts to gain insights into the nature of uncertainty in the studied system.
Doğru cevap:
E) Statistical moments like the mean and variance provide essential information about the central tendency and dispersion of a distribution, guiding the selection and parameter estimation of distributions for modeling uncertainty.

In finance, variance measures the risk of an investment portfolio or an asset. It is a statistical measure of how much the returns on an investment are likely to deviate from their expected value or mean. The sample variance of the return series is a measure that shows how much the asset returns deviate from the sample mean over time. Overall, variance is a critical concept in modern finance because it allows investors to quantify and manage the risk associated with their investments. Variance estimation is directly used in portfolio management, option pricing, and risk measurement.
Doğru cevap:
D) Variance allows investors to quantify and manage the risk associated with their investments by measuring the likelihood of returns deviating from their expected values.

If your answer is wrong, please review the “TIMING ASPECTS OF CASH FLOWS” section.
An annual interest rate is generally employed to find interest rates for regular intervals in a year.

If your answer is wrong, please review the “FUTURE VALUE” section.
Future value of a certain amount of money can be considered as the amount to which an investment will grow after earning interest.

If your answer is wrong, please review the “Future Value” section.
If the compounding is applied more than once a year such that m > 1, then it is called intra-year compounding.

If your answer is wrong, please review the “Future Value” section.

If your answer is wrong, please review the “Present Value” section.

If your answer is wrong, please review the “ANNUITIES: FINITE STREAM OF IDENTICAL CASH FLOWS” section.

If your answer is wrong, please review the “PERPETUITIES: INFINITE STREAM OF IDENTICAL CASH FLOWS” section.

If your answer is wrong, please review the “INFLATION ADJUSTED NOMINAL INTEREST RATES: REAL INTEREST RATES ” section.
Evaluation of cash flows over time is important for economic decision-makers to direct their economic activities.

If your answer is wrong, please review the “Future Value” and “Present Value” section.
Simple or compounding interest rate rules may be applied to find the future values of the present cash flows.

If your answer is wrong, please review the “Future Value” section.
An effective interest rate is the yearly interest rate that would produce the same result after 1 year without compounding.

This question is generated from "introduction" section.
In an environment where investments’ cash flows can be projected correctly, the following six methods are used for evaluation:

1. Net present value (NPV)
2. Profitability Index (PI)
3. Internal Rate of Return (IRR)
4. Modified Internal Rate of Return (MIRR)
5. Payback Period (PP)
6. Discounted Payback Period (DPP)

The correct answer is option B.

This question is generated from the "NET PRESENT VALUE" section.
Net Present Value: The net present value (NPV) method calculates the difference between present values of all benefits and costs for any given investment project. The correct answer is option E.

This question is generated from the Profitability Index (PI) section.
Profitability Index = Present value of future cash flows of the investment / Initial cost of the investment
The correct answer is option A.

This question is generated from the Profitability Index (PI) section.
The Profitability index (PI) is a ratio combined with the net present value ratio to rank investment options with different initial costs. The correct answer is option E.

This question is generated from the Profitability Index (PI) section.
Properties of the Profitability Index

• PI considers all of the cash flows of an investment project during its lifetime and it uses a suitable discount rate.


• When firms face capital rationing, PI provides a useful measure of the efficiency of an investment project.


• When projects are indivisible, and capital rationing is in place, PI may not provide a good measure.


• PI cannot distinguish projects of vastly different scales and may conflict with NPV when evaluating mutually exclusive projects.

The correct answer is option C.

This question is generated from the Internal Rate of Return (IRR) section.
Internal Rate of Return (IRR) is the discount rate that sets the net present value of the investment equal to zero. The correct answer is option D.

This question is generated from the Crossover Rate section.
Properties of IRR

• IRR can be considered as the rate of return on investment and its calculation needs discounting.


• All of the cash flows along the investment’s lifetime are taken into account.


• Projects with IRRs greater than the costs of capital are viable investment projects.


• Its calculation is complex.


• Investment projects with non-conventional cash flows may have multiple IRRs.


• The existence of multiple IRRs renders IRR criterion unreliable and not usable.

The correct answer is option B.

This question is generated from the MODIFIED INTERNAL RATE OF RETURN (MIRR) section.
Advantages of MIRR over IRR: The investor chooses the reinvestment rate in the calculation of
MIRR. In contrast, IRR is determined by the investment’s cash flows only. The correct answer is option A.

This question is generated from the Payback Period with Discounted Cash Flows: Discounted Payback Period (DPP) section.
The Payback Period Decision (accept/reject) Rule

• Accept if the payback period < maximum acceptable payback period.


• Reject if the payback period > maximum acceptable payback period.

The correct answer is option D.

This question is generated from the MODIFIED INTERNAL RATE OF RETURN (MIRR) section.
Decision Rule: Modified Internal Rate of Return

• Accept the project if MIRR > cost of capital r (discount rate) (required rate of return)
• Reject the project if MIRR < cost of capital r (discount rate) (required rate of return)

The correct answer is option A.

The contract is not standard in terms of content and maturity. They are tailor-made between parties. Generally, there’s delivery at maturity or net settlement. Counterpart risk is minimized.
The answer is A.

The contract is standard in terms of both content and maturity. The contract is formal and binding. The risk of default is eliminated via the collateralization mechanism. Generally, the contract is exchanged in the secondhand market before maturity.
The answer is D.

Types of Swaps
i. Interest rates: Interest rate swaps are the most common type of swap contracts, where two parties exchange cash flows based on different interest rates. For example, one party may agree to pay a fixed interest rate to the other party in exchange for a variable interest rate.
ii. Currencies: Currency swaps involve the exchange of cash flows based on different currencies. For example, one party may agree to pay a fixed amount of U.S. dollars in exchange for receiving a fixed amount of euros.
iii. Commodities: Commodity swaps involve the exchange of cash flows based on different commodities, such as oil, natural gas, or metals. For example, one party may agree to pay a fixed price for a certain amount of oil in exchange for receiving a variable price based on the market price of oil.
iv. Equity: Equity swaps involve the exchange of cash flows based on the performance of stocks or stock indices. For example, one party may agree to pay a fixed amount based on the performance of a stock index while receiving a variable amount based on the performance of individual stocks within the index.
v. Credit: Credit default swaps involve the exchange of cash flows based on the credit risk of a particular bond or security. For example, one party may agree to pay the other party if a particular bond defaults.
The answer is E.

The most popular derivative contracts are interest rate derivatives, followed by foreign exchange contracts. The answer is E.

Exchange-traded markets and over-the-counter (OTC) markets are two types of financial markets. Here are some key differences between the two:
i. Trading Process: In exchange-traded markets, buyers and sellers trade securities through a centralized exchange where the trades are executed and cleared by a third-party exchange. On the other hand, in OTC markets, buyers and sellers trade directly with each other, often through dealers or brokers, without needing a centralized exchange.
ii. Regulation: Exchange-traded markets are typically more regulated than OTC markets. Exchangetraded securities are subject to strict regulatory requirements and oversight, which helps to ensure fair and orderly trading and investor protection. In contrast, OTC markets are generally less regulated, which may result in greater investor risk.
iii. Standardization: Exchange-traded security has specific standards regarding maturity, form of delivery, product quality, etc.
The answer is D.

The spot market, also known as the cash market, is where financial assets are traded for immediate delivery and payment. On the other hand, derivative instruments derive their value from underlying assets such as securities, commodities, or currencies. Most of those underlying assets are spot market instruments.
Derivatives allow investors to hedge against price movements in the underlying asset or speculate on future price movements. In the derivatives market, the value of a derivative instrument is determined by the underlying asset’s price. The settlement in these instruments is done at prespecified future dates. Derivative contracts contain all the details regarding the execution of a specific contract, such as maturity, delivery conditions, and the price at which the underlying asset will be exchanged.
Another key difference between the spot and derivative markets is the level of risk involved. In the spot market, investors are exposed to the price risk of the underlying asset. However, in the derivative market, investors are exposed to the risk of the price movements of the underlying asset as well as the risk of the financial instrument itself.
Overall, the spot and derivative markets serve different purposes and are used by investors for different reasons. The spot market is used for immediate transactions, while the derivative market is used for hedging or speculation.
The answer is C.

A swap is a financial agreement between two parties to exchange cash flows based on a predetermined set of terms.
The answer is B.

An option contract is a financial contract between two parties, where one party (the holder or buyer of the option) has the right, but not the obligation, to buy or sell an underlying asset at a specified price (the strike price) and a specified date (the expiration date).
The answer is B.

The margin mechanism in futures markets is designed to guarantee that investors have enough funds to cover any losses they may incur in their futures trading activities. This mechanism involves three components: initial margin, maintenance margin and variation margin. To initiate a futures position, investors are required to deposit a certain sum of money known as the “initial margin” with their broker. The amount of initial margin required varies depending on the type of futures contract, the exchange, and the volatility of the underlying asset. There is no single formula but usually 3-4 times the daily standard deviation of the underlying asset can be considered as a good measure. The maintenance margin, on the other hand, is the minimum amount of money that must be kept in the trader’s account to keep the position open. If the value of the position falls below the maintenance margin level, the trader will be required to deposit additional funds to bring the account back up to the initial margin level. Variation margin is another form of margin mechanism used in futures markets to manage the risk of loss resulting from the daily price movements of the underlying asset. As the value of the futures contract f luctuates daily, the variation margin is calculated and exchanged between the trader and the broker to account for the changes in the position’s value. If the value of the futures contract decreases, the trader will be required to deposit additional funds to cover the loss, which will be held as variation margin by the broker. T he purpose of variation margin is to ensure that the trader always has enough funds to cover the potential losses resulting from daily price movements in the futures market. This mechanism helps to mitigate the risk of default by either party and ensures that the position is constantly collateralized to protect both parties. It’s important to note that while variation margin helps to manage risk, futures trading is still considered a high-risk activity and traders should always have a clear understanding of the risks involved before engaging in futures trading.
The answer is C.

In forwards, there are two common parties - buyers and sellers of a given contract. The party who buys the contract with a specified price and date in the future is known as the long position holder. Conversely, the party who sells the contract for a given price and maturity is known as the short position holder.
The answer is A.

Prepaid Expenses are current assets

Current Assets can include items such as Cash and cash equivalents, Marketable securities, Accounts receivable, Inventories, and Prepaid expenses. Non-Current Assets that you expect to be used for numerous years can include items such as Equipment, Machinery, Vehicles, Buildings, Land (previous items may also be grouped as PPE-Property, Plant and Equipment), Accumulated Depreciation, Intangibles, and Longterm Investments.

Equity: financing that has come from the owners of the company

The Cash Flow statement is a relatively recent addition to the statements and like the income
statement it also covers a period of time.

Net Profit Margin (NPM)=Net profit/Net sales

Companies may have different classes of stock, we will be focusing on the most widely found of these shares which are called common stock. Common stocks typically have these rights:
1. The right to share proportionally in the dividends of the company,
2. The right to share proportionally in the distribution in case of liquidation of the company,
3. The right to vote on important issues affecting the company and elect members to the board of directors,
4. The pre-emptive right prevents the dilution of existing shareholders’ share of ownership against their wishes.

Growth stocks: stocks that pay low or no dividends but whose prices increase at high rates. As a result, all or most of their returns come from capital gains.

Strong form of the EMH states that all privately and publicly available information is fully reflected in prices. If strong form efficiency holds, it should not even be possible for insiders like managers, owners, bankers, politicians, or judges to use private information to obtain consistent excess profits. Even insiders trading on their information (independent of legal and ethical considerations) would be engaging in useless activities.

Accounts Receivable is included in the current assets part of a balance sheet

Liquidity Ratios
• Current ratio=Current assets/Current liabilities
• Quick or Acid-test ratio=(Current assets-Inventory)/Current liabilities

Çözüm için bakınız:
Ünite: 8
Denklem: 1.2
Sayfa: 242

The yield to maturity (YTM) of zero-coupon bonds can be directly calculated using:
γ=(F/P )^1/Tm −1
This is not the case for coupon bonds, which generally require iterative or numerical methods.

In environments where both interest rates and coupon payments change over time, each cash flow must be discounted using its respective rate and time period. This avoids mispricing due to interest rate variations.

When YTM cannot be solved explicitly, it can be approximated using linear interpolation between two yields that bracket the bond price, as described in Equation (2.5) of Unit 8.

Higher coupon payments increase the present value of earlier cash flows, pulling the average maturity of cash flows forward, thus decreasing duration.

Fixed-rate long-term bonds suffer in value as inflation erodes the real value of fixed payments.

Convexity improves upon duration by accounting for the curvature in the price-yield relationship, giving a more accurate estimate of price change for large yield movements

In a premium bond, the price is above face value because the coupon payments are more generous than current market rates, making the coupon rate exceed the yield to maturity

Real value = Nominal × (CPI₀ / CPI₂) = 50 × (1.05 / 1.15) ≈ 45.65

Basically, a bond’s duration measure is formulated as the weighted average of the periods in which the bond’s future cash flows will accrue. Generally, the weight of each period is assigned as the ratio of that period’s discounted cash flow to the cost of the bond, which is its price. The most common measures are Macaulay and modified durations. Macaulay duration measures the number of periods required to recover the cost of a bond, considering present values of all future coupon and principal payments. Modified duration adjusts Macaulay duration to measure the responsiveness of a bond’s price to interest changes