back start next[start] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [ 29 ] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] 29 E+(\-t)lIt should be noted diat in terms of die time diagram, diis is equivalent to bringing the entire amount of interest / onto the time diagram at time t instead of time 1. The expressions + (1 -0/is often called die "exposure associated widiS,."19. Derive formula (5.20).20. Find an expression for die total net contributions during die n periods in formula (5.18).5.6 Time-weighted rates of interest21. In Example 5.9 assume diat May 1 is changed to June 1 and November 1 is changed to October 1.a) Would the yield rate change when computed by die dollar-weighted mediod?b) Would the yield rate change when computed by die time-weighted method?22. In Example 5.9 assume diat everydiing is unchanged except diat an additional \$5000 is wididrawn on July 1.a) Recompute die yield rate by die dollar-weighted mediod.b) The yield rate by die time-weighted mediod cannot be calculated. Explain why not.23. Deposits of \$1000 are made into an investment fiind at time 0 and time 1. The fiind i balance is \$1200 at time 1 and \$2200 at time 2.a) Compute the annual effective yield rate computed by a doUar-weighted calculation.b) Cwnpute die annual effective yield rale which is equivalent to diat produced by ] a time-weighted calculation.24. Let A be die fiind balance on January 1, die balance on June 30, and die balance on December 31.25. 26.4>28. 29.I 30.I 31.investment expenses of \$5000. Find the net effective rate of interest yielded by the funds.16. A fund earning 4% effective has a balance of \$1000 at the beginning of the year. If \$200 is added to the fund at the end of three months and if \$300 is withdrawn from the fund at the end of nine months, find the ending balance under the assumptioni-,, = (i -0.17. a) Under the assumption that j ,(, = (1 - f)/, find an expression for (ig. b) Under the assumption that ,/o = expression for , ,/,.18. Let the exposure associated with / (i.e. the denominator of formula (5.13)) be denoted by E. By using formula (5.17) show diat die force of interest at any point is given bya) If there are no deposits or withdrawals, show that yield rates computed by die dollar-weighted mediod and die time-weighted method are bodi equal to (C - A)IA.b) If there was a single deposit of D immediately after the June 30 balance was calculated, find expressions for the dollar-weighted and time-weighted yield rates.c) Rework ) if die deposit occurred immediately before die June 30 balance was calculated.d) Verbally interpret die fact that die dollar-weighted yield rates in ) and (c) are equal.e) Show that the time-weighted yield rate in ) is greater than in (c).5.7 Portfolio methods and investment year methodsFindijj from the data in Table 5.2 assuming the first payment is made in calendar year + 3.ft is known diat 1 + if = (1.08 -I- .0050* "" for integral 1 < < 5, and integral y,0