Participation Rate

I thought I understand what the participation rate means in an equity-indexed life insurance policy until one day I saw an Aviva's illustration showing one strategy is 130% participating in S&P 500 index. How is that possible?

I revisited the missed fortune book. On page 357 and 358, it talks about the participation rate.
My initial understand of participation rate is that the percentage of your account value participated in the stock market. So I was assuming the maximum value of participation rate has to be 100%.

Now by reading the explanation on the book again. It looks like the math is much more complicated. Let's use the same example in the book and see how a 130% participation rate is possible.

Account Value - $10,000
Cost of buying call options for each $1,000 S&P 500 shares - $50
In order to achieve the 130% participation rate, it needs to purchase $10,000 * 130% = $13,000 S&P shares. This equals ($13,000 / $1000) * $50 = $650.

So we are talking about $650 / $10,000= 6.5% return is used to participate in the S&P 500.
Assuming the guaranteed return is 3%. Aviva has to earn 9.5% in its general account for it to be able to provide this type of participation rate.

Mr Douglas also mentioned on page 357, participation rate and linking method are simply functions of dollars and cents in the overall market for call options, and can hardly be used to differentiate between a good and a bad product.

But if a company only offers 50% participation rate, using the above example,
At 50% participation rate, it will purchase $10,000 * 50% = $5,000 S&P shares. This equals to ($5,000 /$1,000) * $50 = $250
$250 / $10,000= 2.5%

If Aviva is earning 9.5% in its general account, does it mean the interest crediting is this:

• 3% guaranteed return
  
• 2.5% return will be used to participate in S&P 500
  
• the rest of them, 4% is still with the general account.
  

To compare both head to head:

Product	130% Participation Rate	50% Participation Rate
	3% Guaranteed	3% Guaranteed +4% Participated in the general account
	S&P 500 Return on the 6.5%	S&P 500 Return on 2.5%

I have absolutely no idea which will be better. It will all depend on the actual S&P 500 return. But I will generally agree the higher participation rate, the better. This does not seem to be aligned with what Douglas was saying.

My head is spinning. I hope I am not misleading anyone but this is my current understanding now.