Well, obviously not.

From City AM:

HOW THE [HELP TO BUY] SCHEME WORKS

Banks pay the government for a guarantee. If the customer defaults on their mortgage, the government covers almost all of the guaranteed portion.

This guaranteed portion will be up to 15 per cent of the mortgage. In the event of a default, the Treasury will refund the banks for almost all of portion.

The scheme is split into three tranches: 90 to 95 per cent mortgages; 85 to 90 per cent; and 80 to 85 per cent. The fee varies for each, at 0.9 per cent of the loan at the top end, 0.46 per cent in the middle and 0.28 per cent at the bottom end.

It is expected that the fees cover the cost of the scheme and defaults exactly, leaving the Treasury with no profit or loss. If it looks like that break-even point will be missed, the Treasury can raise or cut the fee to match.

OK, that 0.9% is one-off fee for seven years' worth of insurance cover = 0.13% of the loan amount per year, and the sum insured (maximum payout) is 15% of the mortgage (other sources say 15% of the price paid for the home).

They say that the Treasury will break even on this, in other words they do the risk pooling and will have to pay out that 15% on about 1 mortgage in 116 each year (15% sum insured divided by 0.13% average annual charge). We also happen to vaguely remember than on average, only about 1 in 300 mortgaged homes end up being repossessed, not 1 in 116.

This is a risk pooling, not a risk spreading exercise.

Seeing as banks create tens of thousands of mortgages each year and will possibly lose a bit of money on 1 in 116, they can self-insure. All they have to do is charge high loan-to-value borrowers an extra 0.13% interest put take a small part of the total interest (call it 5%) paid by good borrowers and use it to cover their own losses.

But they weren't doing that themselves and the interest rate charged on high loan-to-value mortgages was much higher than for low loan-to-value mortgages (One per cent higher? Two per cent?).

Therefore we must assume that the risk is considerably higher than the 0.9% fee suggests.

Or possibly the explanation is as simple as this:

The banks do get some cost relief when they make these loans. Instead of facing a hefty capital requirement charge for issuing risky, high loan-to-value mortgages, the government guarantee means they are treated as relatively safe and so cost less.

In other words, the government is simply disapplying the relatively sensible capital requirement rules (which would lead to less leverage and less gearing up) and telling the banks to get on with Business As Usual.

Or as @notayesmanecon puts it:

Borrow at 0.75 per cent (FLS), lend at 5 (Help to Buy), get taxpayer backing. What can go wrong for banks?