Synthetic equity?

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BMiller12

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If we use capm to price the underlying stock/index in the long futures component, doesn’t that reflect the Rf + B(ERP). So doesn’t adding that to a risk free asset to create a synthetic equity double your risk free return and therefore yield a return greater return than just the stock itself? More simply put, wouldn’t going long the equity future alone generate an equity position?
Please, any help would be appreciated. Thank you
 
BMiller12 wrote:If we use capm to price the underlying stock/index in the long futures component, doesn’t that reflect the Rf + B(ERP). So doesn’t adding that to a risk free asset to create a synthetic equity double your risk free return and therefore yield a return greater return than just the stock itself? More simply put, wouldn’t going long the equity future alone generate an equity position?
Please, any help would be appreciated. Thank you
Click to expand...
The price on a future (or forward) contract is the spot price increased by the risk-free rate. (You’ll recall that from Level II; if not, look here: http://financialexamhelp123.com/pricing-forwards-and-futures/.) So being long only an equity future won’t generate the equity return; it generates the equity return less the risk-free rate. But when you add the risk-free asset to that … .
Voilà!
 
1.) How does it generate the equity return less the Rf rate?
2.) doesn’t the stock return itself inherently reflect the Rf rate and the ERP, so why add Rf?
sorry just not following.
 
if beta of the equity futures were 1
rf + beta * ERP = rf + 1 (rm - rf) = rm
I guess this is what s2000 means.
 
Suppose that the equity index spot price is 1,500, and the (nominal) risk-free rate is 4%. The price you will pay for the long position in a 90-day equity index forward is:
1,500 × (1 + 4% × (90/360))
= 1,515
If, in 90 days, the equity index spot price is 1,545, then an investment in the equity index will have generated a 3% return. Similarly, an investment in the equity index forward will have generated a 3% return. The forward return comprises:
  • A 1% (risk-free) return (to get from the 1,500 spot price (at t = 0) to the 1,515 forward price (at t = 90)), and
  • A 2% return on the equity index (from the 1,515 forward price (at t = 90) to the 1,545 spot price (at t = 90))
 
Interesting, hadn’t thought of it like that but i’m with ya. So you’re saying that the Rf component is part of the price, not the return?
 
BMiller12 wrote:Interesting, hadn’t thought of it like that but i’m with ya. So you’re saying that the Rf component is part of the price, not the return?
Click to expand...
Yes, so you have to earn that component on your own between the inception and the expiration of the forward contract.
 
This is an interesting discussion- haven’t thought of equity future returns comprising two components before.
 
S2000magician wrote:
Suppose that the equity index spot price is 1,500, and the (nominal) risk-free rate is 4%. The price you will pay for the long position in a 90-day equity index forward is:
1,500 × (1 + 4% × (90/360))
= 1,515
If, in 90 days, the equity index spot price is 1,545, then an investment in the equity index will have generated a 3% return. Similarly, an investment in the equity index forward will have generated a 3% return. The forward return comprises:
  • A 1% (risk-free) return (to get from the 1,500 spot price (at t = 0) to the 1,515 forward price (at t = 90)), and
  • A 2% return on the equity index (from the 1,515 forward price (at t = 90) to the 1,545 spot price (at t = 90))
Click to expand...
TL:DR
Forwards and futures are priced based on the risk free rate. You cannot earn a return on what is already priced in becaused you’re already paying for it.
Hence, you use the risk free rate on your cash to make up that difference to get the return on equity.
 
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