Our market “risk” Measure Position adjusted sensitivity using 1 basis point change Example of “bond risk”: Price (pv): (that’s a total amount of $ the bond is worth) DV01: (how much price moves with a 1/100 of 1% change in yield =.01) amount: (10,000 is 10MM “position”) Position risk: (that’s $9,251 change to position value given a 1bp move) static double bond_risk( const SBB_bond_calculator_interface* bond_calc_ptr, const SBB_instrument_fields* bond_record_ptr, double dv_bump_amount) { double pv = bond_calc_ptr->PV(bond_record_ptr->Yield() ); double dv = bond_calc_ptr->dv_bump(bond_record_ptr->Yield(), pv, dv_bump_amount); double position_risk = bond_record_ptr->Amount() * dv/100.0; return position_risk; }

Units Examples $10,000,000 of a bond 9% coupon, 20 years to maturity - current price: and yield is: 6% Market value is: $10,000,000 * = $13,467,220 Bump yield by up by 100 basis points (1%) and price is now: Our data file has amounts in 000’s so $10,000,000 would be entered as Dollar Value of an “01” (DV01) - price diff between starting yield and 1/100th of a percent move of yield, or 1 basis point, (1/100th of above example). Additionally, it is the average of two shifts: the absolute value of the differences resulting from both an up and down move. “Risk” for us is defined as Amount * DV01/100 and thus stays in thousands since Amount is in thousands. Risk of means for every basis point change in yield we would gain/lose $44,123. double yield_delta_abs = fabs(bump_amount); // yield goes up, price goes down double down_price = PV(base_yield + yield_delta_abs); double price_delta_down = base_price - down_price; // yield goes down, price goes up double up_price = PV(base_yield - yield_delta_abs); double price_delta_up = up_price - base_price; dv01 = (price_delta_up + price_delta_down ) / 2.0;

Bonds are typically priced “relative” Generally: Lower quality is priced relative to higher quality Lower liquidity is priced relative to higher liquidity Relative to what? –Individual bond –Collection of bonds (like an index) “Spread” pricing: –Yield of Treasury = 4.68% –Yield of Corporate = 5.68% –Spread of Corporate = 100bp Spread is measure of credit risk –Base interest rate + spread –Base interest rate + risk premium –Spread = risk premium

Pricing Bonds off a “Yield Curve” Collection of liquid, high quality bonds (like an index) Price using “spread” off matching benchmark bond Match on maturity - the bond’s “remaining term” to “closest” benchmark “Yield Curve” constituent criteria: –Type of Issuer –Issuer’s perceived credit worthiness –Term of maturity of the instrument –Others: optionality, taxability, expected liquidity… The benchmark we will use is: –Current (most recently issued) “Treasuries” –“On-the-run” vs “Off-the-run” Example: –“Trading 30 over the 10 year” –Means: “yield of the quoted bond is 30 basis points more yield than the treasury bond yield which has a maturity of 10 years” “Treasuries” (no credit risk, highest quality, highest liquidity - benchmark to the world) What is the “normal” shape of the “yield curve”? How do the treasury yields come to be? –Fed funds rate, discount rate, auction results

Deliverables for Oct 23 Build a yield curve class 4 bonds in curve: 2, 5,10,30 year maturities Load in new yield curve data file –Special version of existing “data.txt” –Bonds with ticker “T” Load new bond data file which will include a new field: –Spread : “30bp” and tag “SPREAD” or “YIELD” Price and run risk for the book using the curve Our scenarios will be different yield curves: –Parallel up/down, tilts (flatter, steeper)