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5757Kelly Capped by a Max-Loss LimitA binary bet pays net odds 2-to-1 and you estimate a win probability of 0.60, giving a full-Kelly fraction of 0.40. House policy forbids risking more than 25% of capital on a single position. Since a loss costs the full stake, what fraction should you actually bet, and how is it determined?金融与交易中等数值题未尝试免费5758Sensitivity of Kelly Fraction to the EdgeFor a binary bet at net odds b=2, the full-Kelly fraction is f*=(bp-q)/b. By how much does f* change per 0.01 increase in the estimated win probability p? Give the derivative df*/dp and the change for a 0.01 move.金融与交易中等数值题未尝试免费5759Kelly Sizing When the Win Probability Is UncertainFor an even-money bet you are unsure of the true win probability: it is equally likely to be 0.52 or 0.62. A colleague plugs the average estimate 0.57 into the Kelly formula and bets 0.14 of capital. To maximize expected log growth you should instead average the realized growth over the two possible true probabilities. Set up the correct objective and state, with a brief reason, whether the growth-optimal stake is at, above, or below 0.14.金融与交易困难数值题未尝试面试订阅5760Semiannual Coupon Bond PriceA 2-year bond with face 100 pays a 6% annual coupon rate in semiannual installments. Its yield to maturity is 5% per year (compounded semiannually). What is the bond's price?金融与交易中等数值题未尝试免费5761Clean Price From Dirty PriceA bond pays an annual coupon of 5. At settlement, 0.4 of the coupon period has elapsed and the invoice (dirty) price is 103.5. What is the quoted clean price?金融与交易简单数值题未尝试免费5762Macaulay Duration Of A 3-Year BondA 3-year annual-coupon bond has face 100, coupon rate 7%, and yield to maturity 6%. What is its Macaulay duration in years?金融与交易中等数值题未尝试免费5763Price Change From Modified DurationA bond trades at 100 with modified duration 6.2. Using the first-order (duration-only) approximation, estimate the new price if the yield rises by 25 basis points.金融与交易简单数值题未尝试免费5764Convexity Contribution To ReturnA bond has modified duration 7 and convexity 90. For a yield increase of 150 basis points, what is the convexity adjustment alone (the second-order term) as a percentage of price?金融与交易中等数值题未尝试免费5765Current Yield Of A Discount BondA bond with face 100 pays a 4% annual coupon and currently trades at 92. What is its current yield (in percent)? Is it above or below the bond's yield to maturity?金融与交易简单数值题未尝试免费5766Premium, Par, Or DiscountA 2-year annual-coupon bond has face 100, coupon rate 4.5%, and yield to maturity 5.2%. State whether it trades at a premium, par, or discount, and give its price.金融与交易中等数值题未尝试免费5767DV01 From Duration And PriceA bond trades at 98.4 (per 100 face) with modified duration 5.8. What is its DV01 (the price change for a 1-basis-point yield move) per 100 face?金融与交易中等数值题未尝试免费5768Duration Of A Zero-Coupon BondA zero-coupon bond matures in 7 years and is priced at a yield to maturity of 4.5% (annual compounding). What is its modified duration in years?金融与交易简单数值题未尝试免费5769Approximate Yield To MaturityA 4-year annual-coupon bond has face 100, coupon 5, and trades at 95. Using the approximate-YTM formula [C + (F − P)/n] / [(F + P)/2], estimate its yield to maturity (in percent).金融与交易中等数值题未尝试免费5770PV From A Quoted Discount FactorThe market 4-year discount factor is quoted directly as 0.8638. A single cashflow of 250 is due in exactly 4 years. What is its present value?金融与交易简单数值题未尝试面试订阅5771Eight-Year Annuity PVAn ordinary annuity pays 12 at the end of each year for 8 years. The flat discount rate is 0.06. What is its present value?金融与交易中等数值题未尝试面试订阅5772Level Perpetuity PVA perpetuity pays 7 at the end of every year forever, with the first payment one year from now. The discount rate is 0.035. What is its present value?金融与交易简单数值题未尝试面试订阅5773Zero-Coupon Price From YieldA zero-coupon bond pays 100 at maturity in 7 years. Its annually compounded yield is 0.04. What is its price today?金融与交易简单数值题未尝试面试订阅5774Continuous-To-Annual EquivalenceA rate of 0.05 is quoted as continuously compounded. What annually compounded rate produces the same one-year discount factor?金融与交易中等数值题未尝试面试订阅5775Effective Annual Rate From Monthly NominalA nominal annual rate of 0.08 is compounded monthly. What is the effective annual rate?金融与交易中等数值题未尝试面试订阅5776PV Under A Non-Flat Discount CurveA bond pays 50 in 1 year, 50 in 2 years, and 1050 in 3 years. The quoted discount factors are 0.97, 0.93, and 0.88 for years 1, 2, and 3. What is its present value?金融与交易中等数值题未尝试面试订阅