2008 January | 1st Capital Growth

CFA: Trading with the World (16)

LOS 16a: discuss opportunity cost associated with trade, how countries can gain from international trade, how countries determine whether to import, export or produce goods and services, and explain the gains of trade for all parties

opportunity costs associated with trade are the basic costs associated with not trading. if a country were to consume only what they produced, then the opportunity costs limit the amount produced within that country and is generally static. they are said to have identical production and consumption possibilities if they do not trade with other countries. in the text’s example, a country that has trade-offs associated with producing grain vs. producing cars, then the opportunity costs are associated with the increases of one vs the decreases of the other. so if you could create more cars, then how much less grain would you have to produce. trade allows a country to expand the consumption possibilities by increasing production of grain without having to sacrifice less production of cars because of the additional demand that is available by trading with other countries. and if the opportunity cost is high on producing grain but not high on producing cars, then a country would rather import grain and export cars. so the opportunity costs associated with production will determine whether or not something is exported or imported. this generally promotes lower prices globally and increases overall production and consumption, creating economies of scale. so the gains from add’l consumption is not only from domestic consumption, but from consumption abroad. the economies of scale created in the process allow the prices to reach a point where only countries with low opportunity costs export to countries that have high opportunity costs and maintain sound profit levels because of the levels of production and opportunity costs of those countries.

this is called comparitive advantage. the countries trading with each other that are taking advantage of this matching of low vs. high opportunity costs create comparative advantage where everyone wins. by taking advantage of this, countries can maximize profits and increase production by moving outside of the production possibilities frontier. this frontier is the curve of opportunity costs as the slope and the only way outside of that frontier is to trade with other countries and increase production of those products that have low opportunity costs and decrease the production of those products that have high opportunity costs. this is a win-win for all parties involved.

LOS 16b: compare and contrast tariffs, non-tariff barriers, quotas, and voluntary export constraints with respect to international trade

there are 2 major types of international trade restrictions: tariffs and non-tariff barriers (quotas, voluntary export constraints)

tariffs: tariffs basically are taxes. these taxes are implemented on imports. this reduces the amount that the importing country can afford to spend so demand decreases, prices of imports decrease, general inefficiency, reduction of other possibly unrelated export industries as a result of less income/profits generated from free trade.

non-tariff barriers:

quotas: quantitative restriction on the import of a particular good which specifies the max amt of a good that may be imported in a given period of time.

voluntary export restrictions (VER): agreement between 2 countries in which the exporting govt agrees to restrain the volume of its own exports.

this inevitably generates the same results as tariffs do with one key difference. this key difference has to do with who collects the difference in price before and after the restriction. in tariffs, the gov’t collects the tariff in the form of a tax - direct revenue from international trade. in quotas, it goes to the person who has the right to import under the import quota regulations. for VERs, that gap is captured not by the domestic importers, but by the foreign exporter.

LOS 16c: discuss the advantages and disadvantages of protection for each party, and explain the main reasons for trade restriction

the text poses these advantages/disadvantages of protection as arguments for or against and basically states that they are all flawed.

from what I can gather from the text, the major disadvantage of protection is that it reduces the benefits of comparative advantages that any one country may have. it does this by raising the domestic price on imports, lowering the volume of imports and reducing the overall value of imports while equally reducing the value of exports by the same amount.

the text advises of arguments for advantages but states that they are all flawed, so I would assume that implies that there are no advantages aside from maybe allowing for increased gov’t revenue. but this “advantage” has nothing to do with facilitating competitive markets or trade in and of itself. it should be obvious that any type of restriction is going to hamper international markets. this brings us to the second half of the LOS.

trade is restricted because tariffs raise government revenue and because protection brings a small loss to a large number of people and a large gain per person to a small number of people. These are the 2 reasons referred to as tariff revenue and rent seeking. the latter being that lobbyists and other political activists seek to institute these tariffs in order to provide gains for a small number of people. the former is obvious - more taxes, more revenue for the govt.

January 30th, 2008 | Posted in Credit & Economy | No Comments

CFA: Regulation and Antitrust Policy in a Globalized Economy (15)

LOS 15a: discuss the objectives of regulation and the concepts of cost-of-service regulation and rate-of-return regulation

the objectives of regulation are two-fold: to control prices and therefore profits and predatory competition generally existing in monopoly economies, and to control more qualitative factors that including the affects production has on the environment and the quality and safety of the products manufactured. controlling prices/profits is referred to as economic regulation and controlling quality and environmental impacts is referred to as social regulation.

cost-of-service and rate-of-return regulation are types of economic regulation. cost-of-service regulation allows reglulated companies to charge only prices that reflect the actual average cost of providing the services to the customer. rate of return regulation allows regulated companies companies to set policies that ensure a normal, or competitive, rate of return on the investment in the business.

LOS 15b: discuss the benefits of social regulation

the benefits of social regulation are widely difficult to quantify, in the short-term or long-term, subjective, and can span across generations to become fully realized. as the text says, there are just too many to list, the potential benefits, that is. “potential” because of the difficult and subjective nature defining when a benefit is realized and whether everyone agrees that it is indeed realized. reducing the size of the ozone hole, reducing emissions, recycling, etc. are all examples of things that can be encouraged through social regulation. the controversy typically isn’t about whether or not we need to encourage these things, but rather who is going to pay for it - isn’t that always the question? the issue lies who ends up paying - the producer or the consumer? or both? and are the costs outweighing the benefits while not stifling competitive markets? these are the typical questions that enter the argument of social regulation.

LOS 15c: analyze negative side-effects of regulation

in the text, a couple of negative side-effects were defined as creative response and feedback effects. creative response is when the response of the regulation still conforms the letter of the law but undermines what it was intended to accomplish. there are a lot of examples of creative response but i can’t think of any right now. feedback effects are a type of creative response that pertains to the way that someone’s behavior changes after a regulation is in effect. they are very similar but the idea is that a possible side-effect of regulation is the complete ineffectiveness of the regulation or additional problems caused that would require even more regulation or laws to fix, creating what some may think of as a slippery slope of regulation. this is usually the argument of someone that doesn’t think regulations are effective in the long-run, or even short-run.

LOS 15d: distinguish between the different types of regulators behavior

capture hypothesis: the idea of this is that when any regulatory body is setup and inacts regulations, they eventually end up captured by the special interests of the industry or market that is being regulated. this is because when a regulatory body is setup, it needs people from the industry, who also have friends still in the industry which eventually end up being catered to. this leads to incentives being created by special interest groups that tend to reduce the effectiveness of the regulatory body by resulting in regulations that are ineffective at accomplishing their intent. therefore, only the special interest groups’ interest are taken into account when creating and inacting new regulations.

share the gains, share the pains: the regulator’s behavior here is defined by not only the special interest groups, but the consumers and legislators. this idea dictates that a regulator’s specific aim is the keep his/her job. in order to keep his/her job, he/she (ok i’m done with the pronouns for now - he could be a she could be a he) will try his best to keep his boss happy. keeping a regulator’s boss happy means keeping the people happy. so if a regulator bends entirely to the special interst groups, the consumer’s interests are totally lost and suffer. as a result, the consumer complains to the legislators and then the legislators yell at the regulator. so this behavior is more balanced than the “capture” concept.

LOS 15e: discuss the cost of regulation and the effects of deregulation

we have discussed this a bit with some of the negative side-effects and benefits, but yeah, someone has to pay for a bunch of people sitting around a large, round desk and in a similarly round room discussing how to reduce monopolistic profits (increase market competition) or control the amount of greenhouse gases that a company injects into the air. and what about those scientific studies about those greenhouse gases? obviously, consumers are taxed for some regulations and other tax businesses. when businesses are taxed, obviously they can pass down that extra cost to the consumer. its not just taxes, but increasing safety standards at manufacturing plants or requiring that all employees have registered green cards or that they are older than 12 or that they have to not test positive for drugs and the list goes on and on. the things that companies are required to do in order to meet standards or regulations set by regulatory bodies will thereby increase the overall cost of making the products or providing the service ultimately to the consumer. this is pretty straightforward.

deregulation is the removal of regulation - duh! so the effects of deregulation can be categorized into to categories: long-term and short-term. in the short run, there are generally more sudden adjustments that are made to prices, the way producers and manufacturers do business which usually means a drastically different cost structure, and the service consumers may receive. in the long-run the effects of deregulation are lower prices, more competition, and fewer monoplistic profits.

another effect of deregulation has to do with contestable markets. contestable markets are those that can be entered or exited without non-price constraints or high fixed costs. the idea is that by deregulating, you reduce the barriers of entry which allows entrants to enter/exit the marketplace with little or no excess cost that was previously caused by regulations. in the short run, these contestable markets created will increase profits but also increase entrants. the entrants can be capitalizing on easier profits or the inefficiencies of the incumbants in the industry. once competition is restored, these new entrants will be forced out. this is the long run story of contestable markets - is that profits the exceed the opportunity costs of capital (which is now lower because of deregulation) will disappear because the increased number of entrants. this forces companies to increase output, lowering prices (increased economies of scale), and eliminating the excess profits of those that can’t keep up with that level of production. think of walmart. only the strong will survive in the long run.

January 25th, 2008 | Posted in Credit & Economy | No Comments

CFA: Economic Growth (14)

I know that I’m jumping around, but these are the areas that I needed to hit up in their entirety. Frankly, Portfolio Management (the section following Derivatives) is easy. Remember some formulas and concepts and its not too bad.

So, economics is one of those sections that I need to make sure I understand completely. this is probably an easier section for most of you but I have a tendency to confuse facts because I’m trying to memorize them instead of understand them. Remember, this exam you have to really understand the concepts because its too much to memorize.

LOS 14a: discuss the preconditions for economic growth

a suitable incentive system is the most important precondition for economic growth. period.

the institutions that are critical in the development of an incentive system are markets, property rights, and monetary exchange. these social institutions create incentives for people to specialize in the production of goods in which they have a comparative advantage, trade for those products in which they do not, save the profits from trading, and invest those savings into discovering new technologies

markets: facilitate the exchange of information between buyers and sellers and enable them to do business with one another. prices are communicated, which in turn causes the buyers and sellers to adjust quantities that they supply or demand depending on the price. markets cannot be effective without property rights and monetary exchange.

property rights: laws and regulations that govern the right to own, sells and use property. property in this definition is anything that can be bought and sold, including goods and services and factors of production (land, labor, equipment), physical assets, intellectual property, and financial claims. as long as there are property rights, it is assured that the govt will not seize savings and investments.

monetary exchange: provides the efficient exchange of goods and services, including the transfer of ownership of private property from one person to another.

**Scheweser notes that there is no specific form of government that is a pre-condition for economic growth. Which means that dictatorships, communistic as well as democratic countries can all experience economic growth.

LOS 14b: distinguish among saving and investment in new capital, investment in human capital, and investments in new technologies and the way each contributes to economic growth

savings and investment in new capital: increases labor productivity (which is economic growth) by increasing the level of capital per worker (i.e.: machines per worker)

investment in human capital: investment in people’s skill and knowledge and is a key driver in economic growth. both productivity improvements and technological advances derive from investment in human capital. examples: scientific knowledge, written language, on the job work experience that one gains from doing a job

discovery of new technologies: contributes to the sustained economic growth by making human capital and physical capital more productive. R&D is the primary driver of the discovery of new technologies. This includes the development of human capital (more sophisticated scientific knowledge, languages, methods) as well as improvements in the productivity of physical capital (machines to increase productivity).

LOS 14c: discuss labor productivity and the productivity curve, and the effects of changes in capital stock and/or technology on the productivity curve

economic growth = %Change real GDP/labor hour = growth in labor productivity

this is about measuring the productivity or output that a country produces in each hour of labor used as an input. the growth rate of labor productivity changes over time and in order to evaluate the drivers of the changes in growth rate, you have to breakdown this metric into 2 factors: growth in physical capital per labor hour and technological change, and the influence of each can be evaluated separately

productivity curve: curve that results from plotting labor productivity (output/labor hour) is plotted against capital/labor hour at a given state of technology. holding technology constant, this is measuring the effects of capital on productivity. Generally, as capital increases, so does productivity. 2 things are important to understand about the productivity curve:

1. growth in the capital per labor hour causes movement along the productivity curve. since this curve is upwardly sloping, we can say that as capital increases, productivity increases and this increase in productivity represents real economic growth.

2. technological growth causes the productivity curve to shift upwards. productivity increases further as technology increases holding the rate of change of capital constant.

the only caveat in this is that increases of capital per hour consistently decrease the amount of additional productivity gains with each increase of capital per hour. remember, capital is really human capital so adding more people to a job realizes less productivity gains past a certain point. so the curve slopes upwards but gets less and less steep as you move along the curve, adding more and more capital/hour.

LOS 14d: discuss the “One-Third Rule,” and how this rule can be used to explain productivity growth slowdown and speedup

this rule states that a 1% increase in capital/hour results in a 1/3 of 1% increase in real GDP/hour. this rule allows you to separate movement along the curve (increases in capital) and shifts along the curve (increases in technology).

for example: real GDP/hour increases 5% and the capital/hour increases by 4.5%. use the one-third rule in order to determine the amount of real GDP/hour attributable to the increase in capital and the amount attributable to technological change.

growth in capital/hour * 1/3 = 4.5% * 1/3 = 1.5%

this means that for every 1% increase in capital/hour, GDP/hour increases by 1.5%. you know that real GDP/hour increased a total of 5%, so take the difference to determine how much of that 5% is from technological increases.

5% - 1.5% = 3.5% = amount of real GDP/hour attributable to increases in technology, or shifting of the curve.

Productivity slowdown: this occurs when technology is applied to issues other than productivity. this results in productivity not being able to realize the gains from increases in technology.

Productivity speedups: this occurs when there are vast improvements to human capital, technological advances, and/or the growth rate of human capital. this can be achieved by improving education (technology cannot be advance without knowledge), encouraging savings, increased R&D, focused hi-tech industries, and increased int’l trade.

the process of determining the drivers of growth (increases in human capital vs increases in technology) are the same, however. Schweser went through this list of speedups, and so did the text, but the LOS does not say you have to understand the things that speedup growth, only how to apply the 1/3 rule. the method of applying the rule are the same: knowing the rate of change of human capital/hour and GDP/hour, use the method above to breakdown GDP/hour increases by tech vs increases in human capital/hour.

LOS 14e: compare and contrast the classical growth theory, the neoclassical growth theory and the new growth theory.

Going further, the text advises that changes in technology and increases of human capital may be either the cause or the effect of growth in GDP. The basic questions these growth theories try to answer is: what causes economic growth and why do growth rates vary?

classical growth theory:
this determines the relationship between population (human capital growth), the subsistence wage (minimum wage needed to sustain life), increases in technology, and real GDP growth

the basic idea here is that as technology increases and thus increases productivity, which will increase the actual wage above the subsistence wage (which also increases the demand of human capital), which results in an increase (boom) of the population. as a result of the population boom, the actual wage gravitates towards the subsistence wage because now there is more human capital than people can pay for (supply is exceeding demand of human capital) so the wage decreases and moves back to the subsistence wage. if the wage decreases below the subsistence wage, then the population decreases. so the bottom-line is that real GDP growth is always temporary because the real wage will always gravitates towards the subsistence wage as a result of the viscious cycle of resulting population booms causing an excess in the supply of human capital and therefore brings the real GDP growth back to a subsistence level per person.

neoclassical growth theory:
in contrast to the classical growth theory, neoclassical growth theory removes the relationship between population growth and real wages. the entire idea behind real wages gravitating towards the subsistence wage is removed in this theory. this theory spells out the relationship between technology and population growth.

population growth (birth rate) and, coincidentally the death rate, is directly related by income. this is because of the opportunity cost of women’s time. if income rises, the opportunity cost of women having babies and staying home increases because they are giving up more money (opp cost) in order to raise children, which in effect decreases the birth rate. income also affects the death rate by providing better health care and extends lives. neoclassical growth theory says that these opposing forces offset each other in results in population growth being independent of economic growth.

instead of real wages converging into the subsistence wage, you have the real interest rate that converges with the target rate of return. as capital/labor hour increases, the real interest rate has diminishing returns and eventually decreases and converges with the target rate of return. if the real interest rate is higher than the target rate of return, saving is sufficient to make capital/labor hour grow. if the real interest rate is less than the target rate of return, then saving is not sufficient to maintain the current level of capital/labor hour so capital/labor hour shrinks. if they are equal, then saving is sufficient to maintain the current quantity of capital/labor hour.

one major thing to remember is that technological advances as a result of chance. schweser is wrong about this and states that technological advances are a result of real interest rates converging with the target rate of return and this is wrong! the text says nothing about this nor does it say anything about whether or not R&D dollars have failed or succeeded. it also states plainly that “technological change influences the rate of economic growth, but economic growth does not influence the pace of technological change.” this is the point that schweser is trying to make and they are wrong.

neoclassical growth states that growth will advance as long as technology advances and when growth advance, so does prosperity (increased wages). the big difference between neoclassical and classical is that once wages increase, there is no reason for them to decrease because there is no relationship between population growth and real wages. so if technological advances stop, growth will stop but prosperity will not. the reasons why growth will stop are two-fold: first, high profits resulting from technological change bring increased savings and capital accumulation, and second, capital accumulation eventually results in diminishing returns that lower the real interest rate and eventually result from decrease savings and slow the rate of capital accumulation. remember that this theory states that differences in the target rate of return and the real interest rate will determine how much people save.

so technological advances will shift the productivity curve upwards, causing real interest rates to spike and exceed the target rate of return, resulting in economic growth, which causes people to save more and accumulate more capital. if this keeps happening, then the economy will grow indefinitely but once technological advances stop, then the target rate of return will converge with the real interest rate, causing people to save less and stop the accumulation of capital. remember that technological change is a not a result of growth but growth is a result of technological change and technological change occurs by chance. there is no relationship between population growth and economic growth, as in the classical theory.

new growth theory:
the basic concept of new growth theory states that real GDP per person grows because of the choices people make in the pursuit of profit and that growth can persist indefinitely - no diminishing returns as in neoclassical and classical growth theories. in neoclassical growth theory, real interest rates have a diminishing rate of return with increases in savings and the accumulation of capital. in classical growth theory, real wages have a diminising rate of return and converge with the subsistence wage as population grows. in the new growth theory, none of these relationships exist.

new growth theory is based on these core concepts:

discoveries result from choices: this is the choice to pursue discoveries with the intent to increase profits. even though the actual discovery may be by chance, the pursuit of discoveries is a choice with the incentive of making more money in the future. so the amount of people and the intensity upon which they look for discoveries is purely a choice.
discoveries bring profit and competition destroys profits: as stated prior, discoveries will increase profits. however, eventually a new discover is copied, which results in lower profits.
discoveries are a public capital good: public capital goods are those that no one can be excluded from using and when one’s use does not prevent another’s use. once a discovery has been made, everyone can benefit from it. knowledge is an example of a public good.
knowledge capital is not subject to diminishing returns: in all of the theories, production is subject to diminishing returns - add more capital/hour and progressively gain less add’l incremental returns as a result. however, knowledge can increase productivity by applying better methods of production or different machines or whatever. this is central to the unique thing about the new growth theory - there are no growth-stopping machanisms like described in neoclassical or classical! as long as there is knowledge capital, there will be economic growth and can grow indefinitely with knowledge capital.

so everything here starts with knowledge capital. as knowledge capital increases, technological advances will occur and result in higher profits and economic growth. the primary incentive is money (duh!) which causes people to want to innovate in order to realize those profits which leads to new and better products or methods or production which create new jobs which replace/destroy old jobs and industries which results in higher standards of living. people are always wanting a better standard of living so this cycle continues indefinitely forever, spurning indefinite future economic growth.

beware of Schweser at all times and make sure you understand the concepts as stated in the text. don’t assume that Schweser is always right because its not as I have explained in this post.

January 16th, 2008 | Posted in Credit & Economy | No Comments

CFA: Using Credit Derivatives to Enhance Return and Manage Risk (67)

whoooeeee! this is pretty sweet! hope you all feel the same!

LOS 67a: demonstrate the characteristics of a credit default swap, and compare and contrast a credit default swap to a corporate bond

cds are purely credit instruments. while they have payoffs similar to corp bonds, their spreads are purely credit and contain no over return characteristics. as credit tightens and risk increases, spreads widen and as credit loosens and risk decreases, spread tighten.

a cds is an unfunded contract between 2 counterparties, where one counterparty that is buy protection on some underlying bond will pay the credit premium, or spread, to the protection seller.

LOS 67b: explain the advantages of using credit derivatives over other credit instruments

unfunded, unlimited liquidity, more maturities, the exposure can be anything, allows you to short corporate bonds very cheaply.

LOS 67c: explain the use of credit derivatives by the various market participants

banks: typically buy protection in order to hedge their credit risk and increase their capital requirements
hedge funds: can go either way (buy or sell protection), and are the largest growth segment. they employ many different strategies and also provide lots of liquidity in the market
investment banks: typically the market makers. they are the primary source of liquidity in the market.
insurance companies: typically sellers of protection. they are large players in the marketplace. many types of insurance companies invest in cds in order to increase returns or for risk management (hedging).

LOS 65d: discuss credit derivatives strategies and how they are used

basis trading: the text describes this as the difference between the CDS premium and the underlying asset’s swap spread. technically, this is considered the difference between the credit spread on the underlying asset vs the cds spread (premium). capturing the difference between the 2 will result in a duration neutral position that earns whatever that positive difference is. this is not always straightforward because the 2 positions may never match exactly, creating some risk

curve trading: the curve trade can be constructed in two ways: duration and/or default neutral. By having 2 trades, one long and one short, with the same notional, you can have default neutral, but it is not duration neutral. To be duration neutral, you have to adjust the notionals for each side in order to get the durations to be the same. The text gives 2 examples of curve trades: steepeners and flatteners. Steepeners are when you enter into a long 5Y vs a short 2Y, or being long CDS in the long-term and short CDS in the short-term. Flatteners is the opposite, which is long CDS in the short-term and short CDS in the long-term. Steepeners are when investors feel there is long-term issues and Flatteners is when investors feel there are short-term issues.

Index trading: this is trading sets of credits that are packaged and priced as an index. An investor can go short CDS to protect/hedge a bond portfolio or can go long CDS to show a view on sets of credits or combine it with other short Index positions to shows intersector relative-value views.

Options trading: as discussed before, you can reflect a view on credit (single-name or index) or hedge a portfolio of credits with options. a receiver option is the right to sell protection at a specified level at some date in the future and a payer option is the right to buy protection at a specified level at some date in the future. a receiver option is a bullish view on credit and will make money when spreads tighten, while a payer option is the opposite. credit options are typically European options. you can create strangle or straddle strategies with these options, which are typical options strategies.

Capital structure trades: this is where you can combine multiple CDS trades on credits that represent different debt tiers within the company’s overall structure and/or between holding company’s and subsidiary’s debt tiers. there are also strategies that utilize credit vs equity trades, capitalizing on directions that mergers/acquisitions or LBOs may have on the value of either parts of the company’s capital structure. If a company is laying on tons of debt in order to buy a company, then expect spreads to widen while equity prices of the acquiree may increase so you could go long CDS on the acquirer and long equity on the acquiree. There are tons of varieties of these types of strategies.

Correlation trades: this is primarily about default correlation. this is done by going long or short CDX tranches trades. the Index discussed prior is also built into tranches and traded in slices of default correlations just like a CDO. trading different levels of correlation through these tranches is much like trading throughout the capital structure, shorting vs going long on different tiers of debt/equity depending on directions of prices, etc. the difference here is that with the CDX index, there are also synthetic CDX CDO tranches that are built to allow this type of trading. trading these tranches can also be combined with single-name CDS trading to hedge specific name exposures existing in the offsetting CDX synthetic tranches that are in the correlation strategy.

January 15th, 2008 | Posted in Credit & Economy | No Comments

CFA: Interest Rate Derivatrive Instruments (66)

this is almost pointless, but i’m doing it anyways because its going to be on the test.

LOS 66a: demonstrate how both a cap and a floor are packages of options on interest rates, and options on fixed income instruments.

basically, a long cap is equivalent to a call option on interest rates or a put option on a fixed income instrument. a long floor is equivalent to a put option on interest rates or a call option on a fixed income instrument. this is mainly because when rates increase, the value of a cap as well as the value of a call option on rates will increase as well as the value of a put option on a fixed income instrument.

also, the fact that the buyer doesn’t have to pay the seller if rates do not go above the cap rate, in the situation of a long cap. which is similar to an option. if an option is out of the money, a long position is only out the fee and doesn’t have to pay seller anything else after that. if the buyer did have to pay, that would be more like some kind of return swap, where both parties are swapping returns of different instruments.

LOS 66b: compute the payoff for a cap and a floor, and explain how a collar is created.

assuming a cap with a reference rate of 5%, 20MM notional, quarterly pmts (every 3mos)

a buyer of the cap will get paid if the reference rate goes above the cap rate of 5%. assume the rate is 7%: (7% - 5%)*20MM*90/360 = $100,000.

don’t think too much on this formula - this formula is the same for almost anything that has an pmt calculation. the text implies that this payoff calc uses a 30/360 daycount basis.

a collar is the combination of a long cap and a short floor. this in effect creates a band at which the borrower (buyer of cap, seller of floor) can lock in interest rates. if the reference rate exceeds the cap, then the borrower receives a payment, or if the reference rate drops below the floor, then the borrower pays a payment. also, the borrower’s cost will be determined by the net upfront pmt that is paid for the 2 contracts. on a long cap or floor, the buyer pays the seller an upfront. so in this case, there would be a payment paid and a payment received.

January 14th, 2008 | Posted in Credit & Economy | No Comments

CFA: Swap Markets and Contracts (65)

LOS 65a: Distinguish between the pricing and valuation of swaps

pricing is determined by the type of swap it is and how you can make up swap equivalents using other instruments. valuation is the process of taking the price at inception and taking the difference of current market prices to get a net value, positive or negative. generally speaking, all swaps have a 0 value at inception because the price of the swap uses current market prices at inception. value is always the difference of market prices vs the price of the contract at inception.

LOS 65b: explain the equivalence of the following swaps to combinations of other instruments: IRS to a series of off-market FRAs and a plain vanilla swap to a combination of an interest rate call and an interest rate put.

IRS vs series of off-market FRAs: an IRS is a series of fixed and opposing floating payments (assuming a plain vanilla IRS) and a FRA is a one-time fixed payment made at expiration vs. receiving a floating rate payment determined at expiration. Because forwards are priced at inception and only consist of one payment, a swap, which includes multiple fixed payments at the same fixed rate vs multiple floating-rate payments, could be considered a series of off-market forward contracts. This reflects the fact that fixed rate priced at inception of the swap is static and not re-priced as if entering into a forward at the current market price.

plain vanilla swap (IRS) vs. combination of interest rate calls and puts: on expiration of interest rate calls/puts, the cash settlement is the difference between what the strike is and the actual market rate. this methodology is exactly how swaps are valued. so a swap is equivalent to a combination of IR calls and puts with a strike equal to the fixed rate in the swap contract with option maturities equal to the swap payment dates. its also worth noting that this is a combination of buying a call (interest rate cap) and selling a put (interest rate floor). remember that you cannot have a negative value on a long call or put, since a negative (out-of-the-money) call/put will not be exercised so one of the options has to be shorted in order to replicate the negative value if the market rates fall below the rate equal to the strike. this combination of long calls/short puts would result in the transaction buyer to make a net payment if the market prices (rates) are below the strike and a receipt of a payment if the market prices (rates) are above the strike.

LOS 65c: calculate and interpret the fixed rate on a plain vanilla interest rate swap and the market value of the swap during its life

generally speaking, the fixed rate on a plain vanilla IRS is the average of the floating rate term structure throughout the life of the swap. if you are making quarterly swap payments, then the formula is:

(1 - 360day disc rate)/(90day disc rate + 180 day disc rate + 270day disc rate + 360day disc rate)

when finding the disc rate, you use the given LIBOR curve and use the floating rates at each point that matches the payment dates on the swap. in this example its quarterly payments. apply this formula to get the disc rate:

1/(1 + LIBOR*ACT/360).

if the rate is 5.36%, then….

Disc Rate = 1/(1 + .0536*90/360) = .98678

you do this for every point on the curve and then plug those disc rates into the formula for finding the fixed rate.

let’s do an example and assume the points on the LIBOR curve to be:

L90 = .0345, L180 = .0358, L270 = .0370, L360 = .0375

given these points, we are pricing a quarterly IRS.

find the disc rates:

disc L90 = 1/(1+.0345*90/360) = .9914
disc L180 = 1/(1+.0358*180/360) = .9824
disc L270 = 1/(1+.0370*270/360) = .9730
disc L360 = 1/(1+.0375*360.360) = .9639

apply the disc rates to the formula to find the fixed rate:

fixed rate = (1-.9639)/(.9914 + .9824 + .9730 + 9639) = .0092, annualized = .0092*360/90 = .0368

fixed rate = 3.68%

during the life of the swap, valuing it is different than pricing it. let’s say for example, it is 60 days later. Now the payments you are supposed to receive are 30 days, 120 days, 210 days and 300 days away. So you are supposed to use the LIBOR points on those days to come up with the disc factors that you came up with when you priced it. The great thing is that you will be given all of this information in the exam. What is different is that you have to value each leg of the swap, the fixed and the floating, by discounting the known future cash flows to the present assuming a $1 notional and using the disc factors calculated using the new LIBOR term structure. For floating rate instruments, you only know 1 cash flow in the future because its floating and the rate is reset periodically throughout the life of the instrument - hence, the name, “floating rate”. So even though there is a LIBOR term structure (curve) that extends out to 30 yrs, the floating payment will only reset every 30 or 90days depending on what is in the contract and use only that 30 or 90 day point on the curve on the day that it is supposed to reset.

In valuing each leg, you have to keep in mind which leg is paying (-) or receiving (+) and put the appropriate sign for each.

valuing the fixed leg 60 days later:

find the disc rates, apply the disc rates to each future fixed cash flow and assume $1 notional at last payment. the life of the IRS, the fixed leg is going to have 4 future cash flows and assume a $1 notional at the last payment - the dollar notional is critical and will f-up your calcs if you exclude it.

for the sake of ease, i’ll provide the points and disc rates assuming you know how to calc them

disc rates: L30 = .9965, L120 = .9858, L210 = .9751, L300 = .9643

fixed leg: .0092(.9965) + .0092(.9858) + .0092(.9751) + .0092(.9643) + 1(.9643) or
.0092(.9965 + .9858 + .9751 + .9643) + 1(.9643) = 1.0004

floating leg: .0345 is the payment, as dictated in the rate in the original term structure and is the only floating rate payment since th