Why does the stock market rise when the fed induces mild disinflation?

Margins across asset classes equalize. Stocks earn the economic inflation raise, which is high. But they lose the disinflation effect on cash liquidity.  So the cash price of a stock include a slight hike to cover fiat disinflation but the expected economic inflation is already compensated in their pricing power. That is the job of corporations to set  consumer and producer prices, so that result is built in.
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The economy is out of balance, and wants consumer prices up and producer prices down.  That is the positive inflation you see, the economy using price to rebalance itself.  The Fed is likely keep the five year rate too high, induces mild producer price inflation. But the economy knows that and pays the fee to correct it.

So the real economy is trying to get the yield curve a bit steeper for sustainability, rising consumer process and dropping producer prices. Higher taxes and less government spending.  That rebalance stabalizes inventory. The real economic yield curve is kinked up at the short end. But the kink reduced a bit in 2013, mainly because of austerity.  If we keep the deficit at 3%, the economy might allow smaller reserves and velocity rises. But taxes relative to spending in governemt has to be maintained.

The inflation over the last thirty has been mostly ongoing losses  in government passed on to the copnsumer. The Fed has added a mild disinflationary component.