For synthetic cash, the argument is as follows.You are holding stocks in your portfolio, but for the next 6 months, you do not want the equity exposure, instead you are seeking exposure to cash for the next 6 months or so. You may be anticipating a steep decline in the stock market for the next 6 months.
One way to convert your equity exposure to cash for the next 6 months is to do the following. Sell off all the stocks in your portfolio and keep the proceeds (Vp) in T-Bills which will grow at the risk free rate for the next 6 months to Vp * (1+rf)^0.5 and at the end of 6 months sell the T-bills and buy equity back again. But, selling all of your stocks now and investing in Tbills and after 6 months selling off T-bills and buying the stocks again can be expensive because of transaction costs etc.
A better way to accomplish the cash exposure is to use the synthetic cash route. This is accomplished by keeping all the stocks in your portfolio (Don’t sell any stocks) and sell 6 month futures instead. Your position is now long in stock portfolio and short in 6 month equity futures. This is a risk neutral strategy. This risk neutral strategy should earn risk free return over the 6 month period. That is why you should multiply the current portfolio value Vp by (1+Rf)^0.5.