·         Bank risks (regulation horizon for losses): credit risk (1 year), market risk (less than 1 year), operational risk (1 year)

·         Regulatory/economic capital: 

capital required (0.1% chance of loss > capital)/needed (typically less)

·         Deposit insurance (FDIC): %deposit insurance premium, moral hazard (less with 2007 intro of risk-based premiums)

·         Investment banking: private placement (sell securities to a small number of large institutional investors for a fee);

best efforts public offering (sell to the public for a fixed per share fee);

firm commitment public offering (buy & sell to the public for a profit);

initial public offering (IPO) (initial public issuance often at best efforts, sometimes through Dutch auction process);

secondary offerings (additional issuance often target below current market price)

·         Conflicts of interest: separate banking activities (internal barriers); done by US regulation from 1933 to 1999

·         Accounting: separation of trading book (marking to market/model - M2M, proprietary trading) & banking book (loans at cost + accrued interest)

·         Originate-to-distribute model: originating for a fee, selling and servicing the loan for a fee; securitization (portfolio of loan packaging into tranches); pooled & guaranteed by GNMA, FNMA, FHLMC

·         Insurance companies: contract to pay premiums to receive contingent event payouts; life insurance (term, whole …), property-casualty insurance (damage to property, legal liability), health insurance, pension plan insurance; risks include reserves to meet payout falling, default & liquidity of investments, business & operational risks

·         %deadY = conditional probability of dead during year

·         E(payouts) for Y1 to Y2 =

(%deadY1 + (1 - %deadY1) * %deadY2)   * coverage

·         E(premiums) for Y1 to Y2 = 1 + (1 - %deadY1) * premium

·         PV E(premiums) = PV E(payouts)

·         Loss ratio = payouts / premiums

·         Expense ratio = expenses(assess claims, selling) / premiums

·         Combined ratio = loss ratio + expense ratio

·         Operating ratio = combined ratio adjusted for investment income

·         Moral hazard: change in behavior because of insurance availability (decrease it by deductibles, co-insurance provision, policy limit)

·         Adverse selection: select/attract more bad risks than good because of lack of info (decrease by more info, discrimination)

·         Mortality/longevity risk: live shorter/longer; could be hedged or insured

·         Capital requirements & asset liquidity:  property-casualty > life insurance

·         Insurances contribute (%premium income) to a guaranty association if insolvency of member occurs & they are mostly state regulated

·         Defined benefit pension plan: pension defined, pooled, employer responsibility

·         Defined contribution pension plan: pension not defined, individual, employee responsibility

·         Net assets value (NAV) = (portfolio value) / (number of shares); front-end/back-end load, annual fees (expense ratio)

·         Fund fees: (A plus %P) = %A + %P * (%R - %A) = management fee + incentive fee

1.        Open-end mutual funds: shares bought from/sold to fund; valued once per day (4pm); taxes based on fund assets

2.        Closed-end mutual funds: fixed number of shares outstanding traded on stock exchanges; NAV > trade price (fund manager fees)

3.        Exchange-traded funds: for large institutional investors (mostly track indexes); shares could be bought from/sold to the fund but also traded on stock exchanges; exchange in cash or assets; value twice a day; lesser fees

4.        Hedge funds: less regulated, higher fees; incentive fee applicable only over hurdle rate (clause) or previous loss deduction (high-water mark clause); part/all of previous incentive fees retained to cover current losses (clawback clause); after stat & fee adjustments hedge fund returns = mutual fund returns

·         Hedge fund strategies: long/short (undervalued/overvalued) equity (dollar/beta/sector/factor neutrality); dedicated short; distressed securities (distressed debt can’t be shorted); merger arbitrage; convertible arbitrage; fixed income arbitrage (relative value, market-neutral, directional); emerging markets (local exchange, ADRs/underlying, Eurobonds); global macro (disequilibria); managed futures (commodities, technical/fundamental analysis)

1.        Exchange traded markets: smaller centralized market; more (liquid) standardized contracts; less credit risk (exchange clearinghouse)

2.        Over the counter (OTC) markets: larger dealer (concentrated) market over phone/computer; less (illiquid) customized, flexible, negotiable contracts; more credit risk (bilateral or CCP)

1.        Forward contract: OTC obligation; Long = St - K, Short = - Long

2.        Futures contract: exchange-traded obligation (symmetric return)

3.        Option contract: right at exercise/strike price for a cost (option premium); American/European until/at maturity

Profit = Payoff - Premium (asymmetric return)

Long Call holder = Max(0, St - K) - C, short Call writer = - long Call

Long Put = Max(0, K - St) - C, short Put = - long Put

1.        Hedgers: reduce or eliminate financial exposure; if long exposure take short forward (fixe price) or hold put option (downside insurance)

2.        Arbitrageurs: locking riskless profit in temporary mispricing through offsetting

3.        Speculators: gain financial exposure; leverage with the use of derivatives (only margin/premium as initial investment)

1.        Treasury Bonds: $100 000

2.        Eurodollars: $1 000 000

3.        S&P 500: 250X or 50X; NASDAQ 100: 100X

4.        Gold: 100 troy ounces; Silver: 5 000 ounces

5.        Copper: 25 000 pounds

6.        Corn, wheat: 5 000 bushels

7.        Crude oil: 1 000 barrels

·         Futures: quality of asset, contract size, delivery location, delivery time, price quote & tick size, position & price (up/down) limit, open interest, settlement price (closing period average)

·         Margin: initial also clearing (cash + interest or securities)/maintenance/variation margin, mark-to-market, margin call

·         Orders: market, limit, stop-loss, stop-limit, market-if-touched; discretionary (market-not-held), time-of-day, open (GTC), fill-or-kill

·         Futures termination: delivery, exchange for physicals, cash-settlement, close/reverse/offset

·         Normal/inverted futures market: in contango/backwardation, increasing/decreasing futures prices with maturity at point in time

1.        Short hedge: being short the futures & owning an asset

2.        Long hedge: being long the futures & willing to purchase an asset in the future (anticipatory)

Hedging: (+) reduce risk

1.        (-) shareholders can hedge or diversify (no need)

2.        (-) higher risks when competitors do not hedge (profit volatility)

3.        (-) costs of inputs are passed to prices (no need)

4.        (-) informational asymmetry in loss/gain recognition (bad>good)

·         Basis = Spot Price - Futures Price, converge (zone) to 0; Strengthening: larger (+), dS > dF, unfavorable to long; Weakening: smaller (-), dS < dF, favorable to long

·         Basis risk (change in basis): interruption in convergence, change in cost of carry model, imperfect correlation (maturity/duration, liquidity & credit risk mismatch); derivative liquidity & basis risk  tradeoff

·         Rolling the hedge (stack & roll): close & replace with later maturity contract; rollover risk is old + new basis risk

·         Optimal minimum variance hedge ratio (HR or MVR) in cross-hedge: ; minimizes variation/risk; beta(dS,dF), slope of dS against dF regression

·         Hedge effectiveness (coefficient of determination):

%

·         Tailing the hedge adjustment (daily settlements):

HR = %HR * S / F

where %HR: beta (%dS,%dF), slope of %dS against %dF regression

%HR = nbF/nbS * F / S (usual beta)

nbFc = %HR * S/F  * nbS/ Fcs =  %HR * Sv / Fcv

·         Target beta:  (+) long, (-) short

nbFc = (betaTarget - beta) * (Sv / Fcv)

nbFc = HR * nbS / Fcs

HR = nbF / nbS

·         Close to risk free rates: Treasury (too low because regulation, taxes), LIBOR, overnight & term repo (implied), overnight indexed swap (OIS)

·         Discrete compounding expressed continuously (equivalent):

        &

ln(a * b) = ln(a) + ln(b) & ln(a^b) = b * ln(a)

·         Zero spot rate, coupon rate, yield to maturity (YTM)

·         Par yield:  c = (1 - endDF) * m / sum(DFs)

·         Forward rate: forward curve above/below is upward/downward spot curve

·         Expectation theory F = E(S), market segmentation theory, liquidity preference theory F = E(S) + premium

·         Forward rate agreement (FRA): RK & Rforward on (T2 - T1) period compounding; based on LIBOR;

receiving/paying is selling/buying the FRA

1.        Macaulay duration (weighted-average maturity):

continuous compounding = modified duration

2.        Modified duration: for non-continuous compounding with frequency m; for small parallel yield shifts

3.        Dollar duration: DV01 = 1 bp change in interest rate

4.        Convexity effect: in addition to duration

5.        Consol duration: 1/r

6.        Effective duration:

1.        Investment asset forward/futures price:

                 or

2.        Consumption asset forward/futures price:

       or

·         Interest rate parity (IRP):

FX quotation: [base currency]/[quote currency],

inverse of math unit convention

·         Value of long forward/futures:

        or      

1.        Cost of carry model:

c = interest + storage (carrying) costs - cash

y = convenience yied

Contango: F0 > S0 when c > y (normal curve)

Backwardation: F0 < S0 when c < y (inverted curve)

Futures delivery options: in the short position interest if c > y deliver early, if c < y deliver late

·         Forward/futures prices: same for small maturities when uncorrelated with constant (not volatile) interest rates (with positive correlation futures > forwards)

2.        Expectations model: in normal backwardation theory speculators are net long & hedgers are net short; systematic risk impact

               &

Normal contango:

F0 > E(St) when negative systematic risk & r > k

Normal backwardation:

F0 < E(St) when positive systematic risk & r < k

·         Accrued interest =

(days from last coupon to settlement date) / (days in coupon period)

·         Cash/full/invoice/dirty price =

quoted/flat/clean price + accrued interest (AI)

·         Day count conventions:

Treasury bonds (actual/actual),

corporate & municipal bonds (30/360),

Treasury bills, money market (actual/360)

(30 days: Apr, Jun, Sep, Nov)

·         Cash to short = quote futures price * conversion factor (CF) + accrued interest (AI)

·         Conversion factor (CF) = (PV of bond - AI) / face value;

semi-annual bond rounded down to 3 months at 6% YTM with maturity > 15 years (non-callable) on first day of delivery month

·         Cheapest to deliver (CTD) bond: MIN(quoted bond price - quoted futures price * CF);

if yields higher/lower than 6%, deliver high/low duration bonds (low/high coupon, long/short maturity);

if upward/downward sloping yield curve, deliver long/short maturity bonds

·         Discount rate (T-bill quote) = 360 / actual * (100 - P)

annualized % of face value

·         T-bond quote: 100-n/32nds

·         Eurodollar futures price quote: 100 - R (1 bp change = $25 change)

·         Eurodollar futures contract price =

10000 * (100 - 0.25 * (100 - quote)) = 10000 * (100 - 0.25*R)

with continuous compounding

·         LIBOR zero curve:

·         Duration-based hedge: for small parallel shifts in interest rates

nbFc = (DSTarget - DS) / DF * Sv / Fcv

·         Plain vanilla interest rate swap: long (borrower, swap payer) pays fixed & receives floating; short (lender, swap receiver) pays floating & receives fixed; notional not exchanged; today overnight indexed swap (OIS) rate used for discounting but LIBOR to determine CFs (dual-curve stripping); swaps used to transform assets/liabilities; dealer makes bid-ask spread on pair of offsetting swaps

·         Confirmation: legal agreement drafted by the International Swaps & Derivatives Association (ISDA)

·         Absolute/comparative advantage: comparative advantage in lower diff; opposite for other party;

total mutual gain = diff(FIXED) - diff(FLOAT)  reduced by intermediary spread (party gain divided by 2) between fixed rates; arbitrage should erode differentials but they still exists because of creditworthiness (LIBOR +  adjusted spread)

·         Swap credit risk: when positive swap value, lower because of notional amounts, higher in currency swaps

·         Other swaps: equity swap (capital gains & dividends, CFs known at the end), swaption (option on swap), commodity swap, volatility swap, exotic swaps

1.        Interest rate swap: (series of FRAs)

 &

2.        Currency swap: (series of foreign currency forwards)

fixed-for-fixed, fixed-for-floating (fixed currency + interest swap), floating-for-floating (fixed currency + 2 interest swaps); currency asset/liability transformation (no netting); currency swap

&

S0 equates principals at initiation (not at termination)

·         Exchange: product standardization (liquidity), trading venue (price discovery), reporting services (price transparency)

·         Clearing: reconciling & resolving of contracts between parties (after execution & before settlement) through margining M2M (initial & variation margin) & through netting (offsetting contracts/positions)

(1)     Direct clearing: bilateral reconciliation of commitments, netting through payment of differences

(2)     Ring clearing: reduce bilateral exposure & counterparty risk; could be beneficial/detrimental/indifferent to parties involved

(3)     Complete clearing: central intermediation by CCP/clearinghouse which is the counterparty to both sides, loss sharing model

·         Derivatives classes (OTC by notional amount): interest rate > foreign exchange > credit > equity > commodity

·         Systemic risk: chain reaction effect of counterparty defaults due to initial shock

·         Special Purpose Vehicle/Entity (SPV/E): isolates financial risk; converts counterparty risk to legal risk; shifts claim priorities under bankruptcy

·         Derivatives Product Company (DPC): highly graded bankruptcy remote subsidiary providing external parties counterparty risk protection against the failure of the parent company; extension to Credit Derivative Product Companies (CDPCs) providing financial guaranties like monoline issurance companies

·         CPP methods: allocate, manage and reduce counterparty risk in bilateral market (conversion to liquidity, operational & legal risks); reduce interconnectedness; provide more transparency; market neutral matched book (conditional market risk); novation by stepping in between parties & replacing 1 contract with 2 others (legal process); multilateral offset; margining (initial/variation margin); auctioning (defaulted member positions); loss mutualization (guaranty/default fund); negative effect include moral hazard, adverse selection, bifurcations & procyclicality

·         Bilateral markets methods: payment netting (also different currencies), close out netting (termination with value offsetting)

·         CPP risks: clearing member default risk, M2M model risk, liquidity risk, operational & legal risk

·         CPP lessons (last 40 years): problems from large price moves, defaults, insufficient margins & default funds, liquidity delays; 3 have failed - Caisse de Liquidation (1974), Kuala Lumpur Commodity Clearing House (1983), Hong Kong Futures Exchange (1987); 3 nearly failed - Chicago Mercantile Exchange & Options Clearing Corporation (1987), BM&FBOVESPA (1999)

·         FX direct quote: DC/FC (indirect quote: FC/DC)

·         net FX exposure (long/short) = FXassets - Fxliabilities + FXbought - Fxsold;

·         $FX gain/loss = $(net FX exposure) * %dFX(volatility), reduced exposure by matching

·         Bank FX trading activities:

(1)     international trade for customers as agent

(2)     foreign real & financial investments for customers as agent & for the bank as principal

(3)     hedging FX exposure (defensive mechanism)

(4)     speculation (high FX risk)

·         On/Off balance-sheet hedging:

match A&L/use forwards

·         Interest rate parity (IRP):

                or

·         Nominal interest rate = real interest rate + inflation

·         Bond indenture: contract issuer/holder; corporate trustee (bank or trust company) acts as fiduciary on behalf of investors

·         Bond categories: public utilities, transportations, industrials, banks & finance companies, international/Yankee issues

·         Bond interest types:

(1)     straight-coupon bonds: participating/income bonds pay more/less than interest according to profit

(2)     floating/variable-rate bonds

(3)     zero-coupon bonds

·         Original-issue discount (OID) = face value - offering price

·         Bond security types:

(1)     mortgage bonds: first lien on issuer properties

(2)     collateral trust bonds: backed by stocks, notes (personal property), bonds (trustee holds collateral)

(3)     equipment trust certificates: equipment owned by the trustee & rented to the borrower

(4)     debenture bonds: claims on all assets; subordinated bonds (bottom claim); convertible/exchangeable bonds (convert in company/other common stock)

(5)     guaranteed bonds: guaranteed by other company

·         Bond retirement types:

(1)     call & refunding provision: fixed price call (buy all or part at fixed price declining with maturity), make-whole call (PV of remaining CFs if higher than par or par value); potential initial protection period;

(2)     sinking fund provision: money applied to progressive partial retirement through lottery redemption at specific price or through buys in the open market

(3)     maintenance & replacement fund (M&R): money applied to maintain the value of the security backing the debt

(4)     tender offers: buying back part or all at fixed price/spread (not in indenture)

·         High yield bonds: speculative grade (bellow Baa/BBB-) junk bonds issued as such or downgraded (story bonds, subordinated debentures, fallen angels, M&A & LBO cases); deferred-interest (DIB)/payment in-kind (PIK)/ step-up bonds pay no interest/additional bonds/increasing coupon over an initial period, reset bonds

·         Issuer default rate = (defaulted issuers) / (all issuers)

·         Dollar default rate = (par value defaulted bonds) / (par value outstanding bonds)

·         Cumulative default rate = cumulative(dollar default rate)

·         Recovery rate = (amount received) / (total obligation);

seniority improves recovery rates

·         Credit risk: credit default risk (probability of default) & credit spread risk (investor risk aversion change)

·         Event risk: corporate event impacting bond value