##probability
*probability is the measure of the likelihood that an event will occur.probability is quantified as a number between 0 and 1.
*independent event
two variables are statistically independent if the product of their marginal distribution is equal to their joint probability.
*conditional probability(bayes)
the conditional probability is the probability of an outcome given/conditional on another outcome.
*mean/expected value
in probability and statistics,**mean**and**expected**value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution.
*variance and volatility
*variance is the expectation of the squared deviation of a random variable from its mean,and it informally measures how far a set of numbers are spread out from their mean.
*the variance is the square of the**standard deviation/volatility**.
*covariance and correlation
*covariance is a measure of the joint variability of two random variables.
*correlation refers to the extent to which two variables have a linear relationship with each other.
*probability distribution
*we characterize a random variable with a probability distribution.
*it is a mathematical function that can be taught of as providing the probability of occurrence of different possible outcomes in an experiment.
*normal distribution
*a very common continuous probability distribution
*the simplest case of a normal distribution is known as the standard normal distribution.it is a special case when mean=0 and volatility=1.
##hypothesis testing
*a method of statistical inference.
*hypothesis tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance.general hypothesis testing framework:
1.define and interpret the null hypothesis and the alternative.
2.distinguish between one-sided and two-sided hypotheses.
3.describe the confidence interval approach to hypothesis testing.
4.describe the test of significant approach to hypothesis testing.
5.define,calculate and interpret type i and type ii errors.
6.define and interpret the p-value.
##regression
*linear regression is an approach for modeling the relationship between a dependent variable and one or more explanatory variables.
*in a linear regression with a singe independent variable,there are two important coefficients:
1.slope coefficient:a measure of the average change in the dependent given a change in the independent variable.
2.intercept:the predicted value of the dependent if the independent variable is equal to zero.
##monte carlo simulation
*simulation studies are used to investigate the properties and behavior of various statistics of interest.the technique is used in econometrics when the properties of a particular estimation method are not know.
*two key stages:
1.specification of the data generating model.
2.estimation of the parameter of interest in the study.
##time value of money
*the principle of the time value of money explains why interest is paid or earned:interest whether it is on a bank deposit or debt,compensates the depositor or lender for the time value of money.
*present value:the current worth of a future sum of money or stream of cash flows given a specified rate of return.
*future value:the value of an asset or cash at a specified date in the future based on the value of that asset in the present.
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##commercial bank
*a financial institution that accepts deposits from the public and creates credit.
*due to their importance the financial stability of a country,banks are highly regulated in most countries.banks are generally subject to minimum capital requirements based on an international set of capital standards,known as the basel accords
##investment bank
*a private company that provides various financial-related and other services to individuals,corporations,and governments such
as raising financial capital by underwriting or acting as the client’s agent in the issuance of securities.
##insurance companies
*insurance is usually classified as life insurance and non life insurance,with health insurance often being considered to be a separate category.nonlife insurance is also referred to as property casualty insurance.
*a life insincere contract typically lasts a long time and provides payments to the policyholder’s beneficiaries that depend on when the policyholder dies.
*a property-casualty insurance contract typically lasts one year(although it may be renewed)and provides compensation for losses from accident,fire,theft and so on.
*a pension plan is a form of insurance arranged by a company for its employees.it is designed to provide the employees with income for the rest of their lives once they have retired.
##mutual fund
*a professionally managed investment fund that pools money from many investors to purchase securities.
##hedge fund
*an investment fund that pools capital from accredited individuals or institutional investors and invests in a variety of assets,often with complex portfolio construction and risk management techniques.
*hedge funds are subject to much less regulation than mutual funds because they accept funds only from financially sophisticated individuals and organizations.
##arbitrageur:use derivatives to take offsetting positions in two or more instruments to lock in a profit
##hedger:use derivatives markets to offset the risk of prices going unfavorably for their ongoing business activities.
##speculators:use derivatives to seek profits by betting on the future direction of market prices of the underlying asset
##broker:an individual person who arranges transactions between a buyer and a seller for a commission when the deal is executed.
##market maker:maintains bid and offer prices in a given security and stands ready to buy or sell lots of said security,at publicly quoted prices.
##central counter-party
*a financial institution that provides clearing and settlement services for trades in foreign exchange securities,options and derivative contracts.
*acts as an intermediary in futures transactions.
*guarantees performance of parties.
*members must post funds with exchange.
*main task is to keep track of transactions,calculate net position of each member daily.
##interest rate
*treasury rates
*the rates an investor earns on treasury bills and treasury bonds.
*treasury rates are risk-free rates in the sense that an investor who buys a treasury bill or treasury bond is certain that interest and principal payments will be made as promised
*libor:a libor quote by a particular bank is the rate of interest at which the bank is prepared to make a large wholesale deposit with other banks.
*repo rates:in a repurchase agreement,the difference between selling price(today)and the repurchased price(tomorrow or later)is called the repo rate.
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##bond
*basic terms
*face value:usually represents the principal or redemption value.
*coupon rate:a coupon payment on a bond is a periodic interest payment that the bondholder receives during the time between when the bond is issued and when it matures.coupon are normally described in terms of the coupon rate,which is calculated by adding the sum of coupons paid per year and dividing it bu the bond’s face value.
*yield to maturity:the internal rate of return earned by an investor who buys the bond today at the market price,assuming that the bond will be held until maturity,and that all coupon and principal payments will be made on schedule.
*compounding:includes interest earned on the interest.
*price terms
*accrued interest:the interest on a bond that has accumulated since the principal investment,or since the previous coupon payment.
*clean price:the price of a coupon bond not including and accrued interest.immediately following each coupon payment the clean price will equal the dirty price.
*dirty price.a bond pricing quote referring to the price of a coupon bond that includes the present value of all future cash flows,including interest accruing on the next coupon payment.
*treasury
*treasury bills:a short-term debt obligation backed by the u.s.government with a maturity of one year or less.
*treasury notes:mature in 2~10 years;treasury bonds:mature in more than 10 years.both make interest payment semi annually.
*duration:weighted average of the times until those fixed cash flows are received.duration also measures the price sensitivity to yield.
*convexity:a measure of the non-linear relationship of bond prices to changes in interest rates.
##forward and futures
*forward
*agreement to buy.sell asset at future time for certain price.
*traded in the over-the-counter market
*futures
*like forward,agreement to buy/sell asset at certain price&time.
*standardized and trades on an exchange.
*require a daily settlement of gains and losses.
*basic terms
*long:means the holder of the position is obliged to buy the underlying instrument at the contract price at expiry.the holder of the position will profit if the price of the underlying instrument goes up,as the price at the contract was lower.
*short:means having the legal obligation to deliver something at the expiration of the contract,although the holder of the short position may alternately buy back the contract prior to expiration instead of making delivery.short futures transactions are often used by producers of a commodity to fix the future price of goods they have not yet produced.
*exchange market
*a derivatives exchange is a central marketplace when participants can trade standardized contracts,including futures and option contracts.
*the over-the-counter market is an alternative to exchanges where counter-parties can engage in trades directly with each other.
*margin is collateral that the holder of a financial instrument has to deposit with a counter-party to cover some or all of the credit risk the holder poses for the counter-party.when the balance in the margin account falls below the maintenance margin,broker executes a margin call.the next day,the investor needs to“top up”the margin account back to the initial margin level.
*price terms
*forward price is the agreed upon price of an asset in a forward/futures contract.
*if the forward price is higher than the spot price,the future curve is said to be normal,or in contango.
*if the forward price is less than the spot price,the futures curve is said to be inverted,or in backwardation.
*forward rate agreement
*a fra is an agreement that a certain rate will apply to a certain principal during a certain future time period.
*the buyer of an fra locks in a borrowing rate,and the seller locks in a lending rate.
*eurodollar futures
*eurodollar is a dollar deposited in a us or foreign bank outside us,
*the most popular interest rate futures contract in the united states is the three-month eurodollar futures contract traded by the cme group.
*treasury bond futures
*in treasury bonds futures contract,any government bond that has more than 15 years to maturity on the first day of the delivery month and is not callable within 15 years from that day can be delivered.
*since the deliverable bonds have very different market values,the chicago board of trade has created conversion factors.
*cheapest to deliver is the cheapest security that can be delivered to the long position to satisfy the contract specifications and is relevant only for contracts that allow a variety of slightly different securities to be delivered.this is common in treasury bond futures contracts.
##swaps
*swaps
*a derivative in which two parties agree to exchange one steam of cash flows against another.
*interest rate swap
*an interest rate swap is a popular and highly liquid financial derivate instrument in which two parties agree to exchange interest rate cash flows,based on a specified notional amount from a fixed rate to a floating rate.
*currency swap
*a currency swap entails the exchange of principal and interest in one currency for the principal and interest in another currency.
##option
*basic term
*an option to buy an asset at a particular price is termed a call option.
*an option to sell an asset at a particular price is termed a put option.
*the price specified in contract is known as strike price.exercise price.
*premium:amount the option buyer pays and the seller receives for granting the specified rights for the specified period under the option.
*moneyness
*in the money:immediate exercise would generate a positive payoff.
*at the money:immediate exercise would generate no payoff.
*out of the money:immediate exercise would result in a loss.
*value terms
*intrinsic value:the amount that it is in the money,and zero otterwise.
*time value:the difference between the price of an option and its intrinsic value is due to its time value.
*european option:can only be exercised at expiration.
*american option:allow the owner to exercise the option at any time before or at expiration.
##securitization
*the process of creating securities by pooling together various cash-flow producing financial assets such as mortgage loans.these securities are then sold to investors.
*mortgage-backed security
*mbs is a type of asset backed security that is secured by a mortgage or collection of mortgages.
*a mortgage loan,also referred to as a mortgage,is used by purchasers of real property to raise fund to buy real estate.
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##systematic risk and unsystematic risk
*systematic risk
*also known as“undiversifiable risk”.
*systematic risk affects the overall market,not just a particular stock or industry.
*beta is a measure of systematic risk of a security or a portfolio in comparison to the market as a whole.beta is used in the capital asset pricing model which calculates the expected return of an asset based on tis beta and expected market returns.
*unsystematic risk
*also know as“diversifiable risk”.
*company or industry specific hazard that is inherent in each investment.
*market risk
*risk arising from changes in market risk factors.include interest rate risk,equity price risk,foreign exchange risk and commodity price risk.
*operational risk
*refers to financial loss resulting from a host of potential operational breakdowns that we can think in terms of risk of loss resulting from inadequate or failed internal processes,people and systems,or from external events.
##credit risk
*the risk of an economic loss from the failure of a couterparty to fulfill its contractual obligations,or from the increased risk of default during the term of the transaction.
*probability of default:describe the likelihood of a default over a particular time horizon.it provides an estimate of the likelihood that a borrower will be unable to meet its debt obligation.
*loss given default:is the share of an asset that is lost if a borrower defaults.
*exposure at default of an obligor.
##liquidity risk
*funding liquidity risk
*relates to a firm’s ability to raise the necessary cash to roll over its debt to meet the cash,margin,and collateral requirements of counterparts and to satisfy capital withdrawals.
*trading liquidity risk
*is the risk that an institution will not be able to execute a transaction at the prevailing market price because there is no appetite for the deal on the other side of the market.if the transaction cannot be postponed,its execution may lead to a substantial loss.
*value at risk
*a measure of the risk of investments.
*measures the potential loss in value of a risky asset or portfolio over a defined period for a given confidence interval.
*risk management process
*the name given to a logical and systematic method of identifying,assessing,treating and monitoring the risks involved in any activity or process.
*risk identification
*defining types of risks
*development of risk profiles
*risk assessment
*how likely is the risk event to happen
*what would be the impact,cost or consequences of that event occurring?
*hedging
*an investment position intended to offset potential losses or gains that may be incurred by a companion investment.
*minimum variance hedge ratio:the ratio that minimizes the variance of the hedged position.
*basis risk:is the risk associated with imperfect hedging.it is the financial risk that offsetting investments in a hedge strategy will not experience price changes in entirely opposite directions from each other.
*enterprise risk management
*an erm function would be responsible for establishing firm-wide policies and standards,coordinate risk management activities across business units and functions,and provide overall risk monitoring for senior management and the board.
*risk appetite
*is a method to help guide an organization’s approach to risk and risk management.the level of risk that an organization is prepared to accept in pursuit of its objectives.
*stress test
*an analysis or simulation designed to determine the ability of a given financial instrument or institution to deal with an economic crisis.
*capital
*while firms set aside reserves in preparation for expected losses,capital is needed to provide a cushion against unexpected loss.
*economic capital
*ec is a var-type measure that represents the amount of capital a firm allocates to self-insurance.
*regulatory capital
*the amount of capital a bank or other financial institution has to hold as required by its financial regulator.