Equitizeing cash vs. Adjusting the Allocationg among Asset Classes

hi folks, i have a question, when you equitize cash, Reading 27example 3(page 237),. you would first use the cash amount of 500 million times by the (1+rfr)^.5 to get the value of the cash at the risk free rate in 6 months, then devide this number the by future price of $1,500 and the multiplier of 500 to get the numbers of contact needed which is 3383. the formula is 500,000,000*(1.03)^.5 / (100x1500) this is fine, i can understand it, but in exmpale 6, (page 246), which is asking to reduce beta of the equity and increase the duration of the bond in the portfolio. what i don’t get is when you reduce the beta, you are essentially shorting the future contract, the formula given in this exmpale is (0-1.05)/(0.98) x (10,000,000/280,000). i understand eveyrthing in this formula except where did the risk free rate go in this exmaple? if the risk free rate is given, should i use 10,000,000x(1+rfr)^t then devide by 280,000? can anyone shine any lights?

I wrote a whole series of articles on this sort of thing: http://financialexamhelp123.com/level-iii-risk-management-applications-of-derivatives/

The short answer is that when you’re changing the equity/fixed income allocation or changing the equity beta or changing the fixed income (effective) duration, you’re not leaving any amount as cash for any period of time: you reduce your equity and Bam! increase your fixed income; it was cash for 3.76 nanoseconds. Not enough time to earn any appreciable interest.