Long term bonds

I should have clarified. When I said long duration funds, I meant funds holding longer tenure Gsecs. No corporate bonds.

Bonds and equities would go down together during periods of rising inflation, since inflation leads to a drop in valuations for every single asset class.(except commodities)

Falling inflation improves valuations for every asset class, so in theory they all should appreciate during such periods. But if inflation is falling due to economic downturn, the earnings would fall too, so equities correct despite an appreciation in valuation. But government bonds on other hand appreciate.