What moves the PCR

An index has 100 lakh units of call OI and 90 lakh units of put OI in one expiry. (a) Compute $\mathrm{PCR}_{OI}$. (b) A pension fund buys 30 lakh units of puts 8% below spot as portfolio insurance; the sellers open new short positions. Recompute the PCR. Has the market become more bearish? (c) Prove Proposition 9A.2(a) and give a numerical example where adding strikes above the forward lowers the PCR.