bilalchughtai's Shortform

Should you invest in a Lifetime ISA? (UK)

The Lifetime Individual Savings Account (LISA) is a government saving scheme in the UK intended primarily to help individuals between the ages of 18 and 50 buy their first home (among a few other things). You can hold your money either as cash or in stocks and shares.

The unique selling point of the scheme is that the government will add a 25% bonus on all savings up to £4000 per year. However, this comes with several restrictions. The account is intended to only be used for the following purposes:
1) to buy your first home, worth £450k or less
2) if you are aged 60 or older
3) if you are terminally ill

The government do permit individuals to use the money for other purposes, with the caveat that a 25% cut will be taken before doing so. Seems like a no brainer? Not quite.

Suppose you invest $x$ in your LISA. The government bonus puts this up to $1.25x$. Suppose later you decide to withdraw your money for purposes other than (1-3). Then you end up with $0.75\times 1.25x=0.9375x$. That's a 6.25% loss!

So when does it make sense to use your LISA? Suppose further you have some uncertainty over whether you will use your money for (1-3). Most likely, you are worried that you might not buy a home in the UK, or you might want to buy a home over the price of £450k (because for instance you live in London, and £450k doesn't stretch that far).

Let's compute the expected value of your investment if the probability of using your money for the purposes (1-3) is $p$ (which likely means your probability of using it for 1 is also about $p$). Suppose we invest £$x$. For our investment to be worth it, we should expect at least £$x$ back.

EV = $p$(bonus scenario) + $(1-p)$(penalty scenario) = $p\left(1.25x\right)+(1-p)(0.75\times 1.25x)\ge x$, implying $p\ge 0.2$.

So, you should use your ISA if your probability of using it to buy a home (or 2,3) is above 20%. This is surprisingly low! Note further this calculation applies regardless of if you use a cash or stocks and shares LISA. 

I havn't ever seen this calculation written up publicly before so thought it was worth sharing.