Financial Market

Three measures of the aggregate price level:

Value at risk is usually quoted in units of $ for a given probability and time horizon

Ex: 1% one-year VAR of $10 million means 1% chance that a portfolio will lose $10 million in a year

The stress test is a test usually ordered by government to see how some firm will stand up to a financial crisis.

Fat-tailed

\[x_t=x_{t-1}+\varepsilon_t\]

• a store of value
• a unit of account
• a medium of transaction

The base interest rate on corporate bank loans, an indicator of the cost of business borrowing from banks.

The interest rate charged on overnight loans in the federal funds market, a sensitive indicator of the cost to banks of borrowing funds from other banks and the stance of monetary policy.

• shortest term interest in the U.S. (overnight rate)
• the most important interest rates in the U.S.
• Fed Reserve Target
• When it is high, it indicates that the banks are strapped for funds; when it is low, banks' credit needs are low
• IOER: the Federal Reserve Banks pay interest on excess reserve balances(IOER)

see: Bloomberg U.S Rate & Bonds

The interest rate on U.S. treasury bills, an indicator of general interest-rate movements.

• the most liquid of all the money market instruments
• the safest of all the money market instruments

The interest rate on a 30-year fixed­rate residential mortgage that is less than $417,000 in amount and is guaranteed by the FHA.

The interest rate on a 30-year fixed­rate residential mortgage for prime customers that is in excess of $417,000 in amount.

The interest rate for the first five years on a residential mortgage that adjusts after five years for prime customers.

The interest rate on a four-year fixed­rate new-car loan.

The interest rate on U.S. Treasury bonds maturing in ten years.

Risk Pooling is the source of all value in insurance.

If n policies, each has independent probability p of a claim, then the number of claims follows the binomial distribution. The standard deviation of the fraction of policies that result in a claim is \(\frac{\sqrt{np(1-p)}}{n}=\sqrt{\frac{p(1-p)}{n}}\)

Yield to maturity(YTM) is the total return anticipated on a bond if the bond is held until it matures.

• Yield to maturity is considered a long-term bond yield, but is expressed as an annual rate

\[P = \frac{M}{(1+r)^T}\]

Fixed-Payment \(FP\) \[P = \frac{FP}{1+r}+\frac{FP}{(1+r)^2}+\cdots+\frac{FP}{(1+r)^T} = \sum_{t=1}^{T}\frac{FP}{(1+r)^t} = \frac{FP}{r}(1-\frac{1}{(1+r)^T})\]

A forward rate is an interest rate applicable to a financial transaction that will take place in the future. Forward rates are calculated from the spot rate, and are adjusted for the cost of carry to determine the future interest rate that equates the total return of a longer-term investment with a strategy of rolling over a shorter-term investment. \[1+f_{k-1\to k}=\frac{(1+r_k)^k}{(1+r_{k-1})^{k-1}}\] \(r_k\) is the \(k\) -period spot rate. \(f_{k-1\to k}\) is the forward rate between \(k-1\) and \(k\) periods

\[1+r_{money}=(1+r_{real})(1+i)\] \(i\) is the inflation rate

• eg: TIP(iShares TIPS Bond ETF)
• UK Indexed-Linked Gilts
• France issued Euro Index bonds

A coupon bond, also referred to as a bearer bond, is a debt obligation with coupons attached that represent semi-annual interest payments

• Yearly payment, Term \(T\), Coupon value \(C\), Par Value(Value at Maturity) \(M\), YTM(Yield to Maturity) \(r\) \[C=M\cdot Coupon\ rate\] \[P = \frac{C}{1+r}+\frac{C}{(1+r)^2}+\dots+\frac{C}{(1+r)^T}+\frac{M}{(1+r)^T}=\sum_{t=1}^{T}\frac{C}{(1+r)^t}+\frac{M}{(1+r)^T}\] \[P = \frac{C}{r}(1-\frac{1}{(1+r)^T})+\frac{M}{(1+r)^T}\]
• six-month payments \[P = \frac{C}{r}(1-\frac{1}{(1+r/2)^{2T}})+\frac{M}{(1+r/2)^{2T}}\]
• calculate bond price between coupon payments

A consol bond is aslo known as a perpetual bond \[Consol\ PDV = \lim_{T\to\infty}P = \lim_{T\to\infty}\frac{C}{r}(1-\frac{1}{(1+r)^T}) = \frac{C}{r}\] A growing consol bond: coupon value will grow at \(g\) rate, means paying \(C(1+g)^{T-1}\) in \(T\). \[Growing\ Consol\ PDV=\frac{C}{r-g}\]

No coupon payments, initially sold at a discount.

• Term \(T\), YTM(Yield to Maturity) \(r\), PDV \(P\)(Present Discounted Value) \[PDV = \frac{1}{(1+r)^T}\]
• Typically, bonds pay interest rate every six months \[PDV = \frac{1}{(1+r/2)^{2T}}\]

Eurobond, a bond denominated in a currency other than that of the country in which it is sold.

Corporate law held by the state governments.

• Blue Sky Laws(1911-1933 47 states): before the centralized regulation of SEC(1934).

SEC, Securities and Exchange Commission

BIS(Bank for international settlement), intermediary of central banks.

Two ideas:

1. An investor's acceptance of risk should incorporate not only the possible losses that can occur, but also the utility, or intrinsic value, of the investment itself
2. marginal utility: The same amount of additional money was less useful to an already-wealthy person than it would be to a poor person.

People decide which outcomes they consider equivalent, set a reference point and then consider lesser outcomes as losses and greater ones as gains

Prospect theory assumes that losses and gains are valued differently, and thus individuals make decisions based on perceived gains instead of perceived losses

\[V=\sum_{i=1}^{n}w(p_i)v(o_i)\] \(o_i\) for outcome, \(p_i\) for probability of particular outcome. \(w(x)\) is the weighting function, \(v(x)\) is the value function. \(U\) is the overall or expected utility of the outcomes to the individual making the decision.

Mental conflict that occurs when one learns one's beliefs are wrong, avoidance behavior.

refers to a situation involving conflicting attitudes, beliefs or behaviors. This produces a feeling of discomfort leading to an alteration in one of the attitudes, beliefs or behaviors to reduce the discomfort and restore balance, etc.

Festinger's (1957) cognitive dissonance theory suggests that we have an inner drive to hold all our attitudes and beliefs in harmony and avoid disharmony (or dissonance). This is known as the principle of cognitive consistency

• Ads for recently purchased cars
• Disposition effect

Humans have a tendency to place particular events into mental compartments and the difference between these compartments sometimes impacts our behavior more than the events themselves

• overfocus on the small part of the portfolio

• social basis of attention

  may everyone pay attention to some stock -> overpriced

• wheel of fortune experiment
• Stock prices anchored to past values, or to other stock prices in same field.

• Tendency to see patterns in what is really random walk
• Stock price manipulators try to create patterns to fool investors

Inability to make a decision that is contingent on future information

• Reaction of stock market to news, make stock strategies to trade on news

The spread of ideas, attitudes, or behaviour patterns in a group through imitation and conformity.

People react to a particular choice in different ways depending on how it is presented

Experiment: fed hungry pigeons mechanically. Pigeons developed superstitions.

• Stock market responses to events may have similar origins

• Tendency to adopt beliefs of other people

A company's book value is its total assets minus intangible assets and liabilities

The idea is the price of stock should be the present discount value of expected dividends.

• if earning equal dividends and if dividends grow at long-run rate \(g\), then by growing

consol model \(P=\frac{E}{r-g}\), \(P/E=\frac{1}{r-g}\) (\(r\) for discount rate)

Companies prioritize their sources of financing:

1. Internal financing
2. debt issuance
3. Equity

• stock dividend

• the reverse of a dilution
• like cash dividend, more tax advantageous

The idea is the price of stock should be the present discount value of expected dividends.

if earnings equal dividends and dividends grow at long-term rate \(g\) \[P=\frac{E}{1+r}+\frac{E(1+g)}{(1+r)^2}+\frac{E(1+g)^2}{(1+r)^3}+\cdots=\frac{E}{r-g}\] \[P/E=\frac{1}{r-g}\]

• \(P/E\) price earnings ratio
• Low \(P/E\) means that earnings are rationally forecasted to decrease in future(low \(g\)) or that risk is high(high \(r\))
• Value investing says invest in low \(P/E\)

\[\mbox{foward rate(CNH/USD)}=\mbox{spot rate(CNH/USD)}\cdot\frac{1+r_{CNH}}{1+r_{USD}}\]

• \(r_a\): actual interest rate on contract date
• \(r_c\): contract rate
• D: days in contract period
• A: contract amount
• B: 360 or 365 days, convension

\[\begin{align*} Settlement & = \mbox{PV of exceeded rate amount on settlement date} \\ & = \frac{(r_a-r_c)\times \frac{D}{B}\times A}{1+r_a\times \frac{D}{B}} \end{align*}\]

• contango: delivering at a future date costs you more
• backwardation: OPP contango

• \(r\): interest rate
• \(s\): storage cost

\[P_\mbox{future}=P_\mbox{spot}(1+r+s)\]

• If commodity is not in a storage(shortage), then is is possible that:

\[P_\mbox{future} < P_\mbox{spot}(1+r+s)\]

• Cash settlement delivery
• Settlement: \(250(Index_t-Futures_{t-1})\)

price of stock = call price + pv of strike + pv of dividends - put price

• computed from option price
• a measure of potential risk in financial markets

investopedia

\[r_i = \beta_i \cdot r_m + \alpha_i\]

Risk free rate of return + excess return

Current prices reflect all past publicly available information.

• Prohibits profit from T.A

Weak + prices instantly change to reflect new public information

• Prohibits profit from T.A & F.A

Semi-Strong + prices instantly reflect even hidden or "insider" information

• Prohibits profit from insider information

• Prices and volume only

• Financial statements
• P/E ratios, cash on hand, dividends

\[return = \frac{value_{end}}{value_{start}} - 1 \]

\[rets_i = \frac{value_i}{value_{i-1}} - 1 \]

\[Sharpe = \frac{E - R_f}{\sigma} \]

• \(R_f\): risk free return

only count volatility when it's downward

• United States Treasury Bills

• Negotiable Bank Certificates of Deposit

  A certificate of deposit (CD) is a debt instrument sold by a bank to depositors that pays annual interest of a given amount and at maturity pays back the original purchase price.

• Commercial Paper

  Commercial paper is a short-term debt instrument issued by large banks and well-known corporations

• Repurchase Agreements

  Repurchase agreements(repos) are effectively short-term loans(usually with a maturity of less than two weeks) for which Treasury bills serve as collateral, an asset that the lender receives if the borrower does not pay back the loan.

• Federal (Fed) Funds

• Stocks

• Mortgages

  Mortgages are loans to households or firms to purchase housing, land, or other real structures, where the structure or land itself serves as collateral for the loans.

  The federal government plays an active role in the mortgage market via the three goverment agencies: FNMA, GNMA, FHLMC. They provide funds to the mortgage market by selling bonds and using the proceeds Lo buy mortgages.

• Corporate Bonds
  • Convertible bonds: have the additional feature of allowing the holder to convert them into a specified number of shares of stock at any time up to the maturity date.

• U.S. Goverment Securities

  These long-term debt instruments are issued by the U.S. Treasury to finance the deficits of the federal government.

  • most widely traded bonds in the United States

• U.S. Goverment Agency Securities

  These long-term bonds are issued by various government agencies

• State and Local Goverment Bonds

  State and local bonds, also called municipal bonds, are long-term debt instruments issued by state and local governments.

  • An imponant feature of these bonds is that their interest payments are exempt from federal income tax and generally from state taxes in the issuing state.
• Consumer and Bank Commercial Loans

• Commercial Banks
• Savings and Loan Associations(S&Ls) and Mutual Savings Banks
• Credit Unions

• Life Insurance Companies
• Fire and Casualty Insurance Companies
• Pension Funds and Government Retirement Funds

• Finance Companies

  Finance companies raise funds by selling commercial paper and by issuing stocks and bonds. They lend these funds to consumers , who make purchases of such items as furniture, automobiles, and home improvements, and to small businesses.

• Mutual Funds
• Money Market Mutual Funds
• Investment Banks

The use of electronic means of payment leaves an electronic trail that contains a large amount of personal data on buying habits.