Should the change in price of a synthetic (long call + short put) ever be different from the change in price of the underlying?

Question

On my paper brokerage account, I can see that this appears to not hold true ...
Daily P&L   Financial Instrument    Position    Last    Market Value    Prior Close Change (Last - Prior Close)
310         SPY                     100         372.1   37,210          369         3.1
178         SPY Dec30'20 369 CALL   1           3.84    383             2.05        1.79
158         SPY Dec30'20 369 PUT    -1          0.63    -63             2.21        -1.58
-310        SPY CFD                 -100        372.1   -37,210         369         3.1
                                
336         Sum of Options portofolio           3.21    320              -0.16      3.37

The SPY and SPY CFD positions do indeed move together; however it seems that my options portfolio supposed to simulate SPY has made 336 today instead of 310.
What is going on? Does it have to do with the spread / fact that it's a paper portfolio? Or is the synthetic only guaranteed to have the same value as the underlying at expiry ... ? Would it have to do with the change in volatility, as VIX is down today ~0.5%? Or something else?

Bob Baerker · Accepted Answer

If you  use last prices to evaluate the P&L of a position, it may be off because of stale quotes (the last trade in the option traded before the SPY closed).
In addition, your Market Value is using the last price so you are  not taking into account the B/A spreads and it's possible that is exaggerating the gain on the synthetic.
Given that the SPY is extremely liquid, it tends to trade with a very narrow spread, often as low as a penny.  Options such as your $369 call have value (today) and currently has a 5-7 cent spread.  Your $369 put is low value so it has a one cent spread.
Friday, these two options were somewhat near each other in price so they each were likely to have a 5-7 cent wide B/A spread.  That's means that at times, your calculation could be off as much as 10-14 cents unless you were properly using the respective bid and ask prices.
Change in implied volatility could also affect the two day comparison.  If IV increased, even though you're long one option and short the other, the detrimental effect on the short put would be less than the beneficial effect on the higher priced long call. All in all, my guess is that this might be pennies, if even that.
The short answer?  Your synthetic is up 19 cents more than the SPY right now but only an in depth examination of real time prices would explain why.

Should the change in price of a synthetic (long call + short put) ever be different from the change in price of the underlying?

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