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1422Approximate Sharpe 14If annual return is 12% and annual vol is 18%, what is the Sharpe ratio under zero funding rate?脑筋急转弯中等数值题未尝试免费1423Taylor PnL Proxy 15Use option PnL ~= Delta*dS + 0.5*Gamma*(dS) 2. If Delta=1200, Gamma=300, and dS=0.4, what approximate PnL results?脑筋急转弯简单数值题未尝试免费1424Contract Count from Notional 16One futures contract has notional 210,000. How many contracts make up 52.5 million of notional?脑筋急转弯中等数值题未尝试免费1425Basis-Point Revenue 17What is 7.5 bp of 640 million?脑筋急转弯困难数值题未尝试面试订阅2721Unit and Domino Tilings of a Nine-Cell StripA strip of length 9 is tiled using monomers of length 1 and dominoes of length 2. Derive the generating function for the number a n of tilings, and compute a 9.脑筋急转弯简单数值题未尝试面试订阅2722Tiling With 1-, 2-, and 4-Step BlocksLet a n be the number of ways to tile a strip of length n using blocks of lengths 1, 2, and 4. Write the generating function A(x) and compute a 10.脑筋急转弯中等derivation未尝试面试订阅2723Execution Schedules With at Most One Large SliceAn execution schedule reaches total size 11 using slices of sizes 1, 2, and 5, but the large 5-lot slice may be used at most once. Order of slices does not matter. How many schedules are possible?脑筋急转弯中等derivation未尝试面试订阅2724Recurrence Hidden in a Rational Generating FunctionLet A(x)=sum n>=0 a n x n = (1+x)/(1-2x+x 3). Derive a linear recurrence for a n and compute a 5.脑筋急转弯困难derivation未尝试面试订阅2725Coefficient in a Mixed Pole Generating FunctionFind the coefficient of x 8 in 1/((1-x) 2(1-x 3)).脑筋急转弯中等derivation未尝试面试订阅2726Subset Count With Cardinality Divisible by ThreeHow many subsets of a 10-element set have size divisible by 3? Solve it with a roots-of-unity filter or an equivalent generating-function argument.脑筋急转弯中等derivation未尝试面试订阅2727Binary Strings With Ones Congruent to One Mod FourHow many binary strings of length 9 have a number of ones congruent to 1 modulo 4?脑筋急转弯简单数值题未尝试面试订阅2728Ternary Strings With a Modular Count of One SymbolHow many strings of length 8 over the alphabet A,B,C contain a number of As congruent to 2 modulo 3?脑筋急转弯中等derivation未尝试面试订阅2729Chip Allocation With a Congruence ConstraintTwelve identical chips are allocated across four desks. How many allocations have the property that the combined chips on desks 1 and 2 are divisible by 3?脑筋急转弯困难derivation未尝试面试订阅2730Submultisets With Size Divisible by ThreeFrom the multiset a,a,a,b,b,c,c,c,c , you may choose any submultiset. How many choices have total size divisible by 3?脑筋急转弯困难derivation未尝试面试订阅2731Coefficient in a Product of Short Generating FunctionsFind the coefficient of x 12 in (1+x+x 2) 4 (1+x 2+x 4) 2.脑筋急转弯中等derivation未尝试面试订阅2732Weak Compositions With Uniform Upper BoundsHow many weak compositions of 15 into 5 parts have every part at most 4? Solve it from the generating function ((1-x 5)/(1-x)) 5.脑筋急转弯中等derivation未尝试面试订阅2733Payment Combinations With an Odd Number of Nine-Unit NotesA cashier can use 2-unit, 5-unit, and 9-unit notes to make total payment 24. The number of 9-unit notes must be odd. Order does not matter. How many valid combinations exist?脑筋急转弯中等derivation未尝试面试订阅2734Weighted Sum With One Binary Heavy BlockHow many nonnegative integer solutions satisfy 2a+3b+4c+6d=20 if d is restricted to be either 0 or 1?脑筋急转弯困难derivation未尝试面试订阅2735Compositions Into Ones and TwosLet c n be the number of ordered compositions of n using only parts 1 and 2. Use a generating function to show c n = F n+1 , and then compute c 10.脑筋急转弯简单数值题未尝试面试订阅2736A Fibonacci Binomial Sum From Coefficient ExtractionEvaluate sum k>=0 C(12-k, k). You should explain why a generating function turns this into a Fibonacci-type coefficient.脑筋急转弯中等derivation未尝试面试订阅