From said former student:
"If you want to work in the rates space; that could be US treasury or emerging markets or end up there in risk, trading or quant area, knowing PCA is extremely helpful. The problem in these areas is the number of time series available. E.g The US treasury desk: There are 1,3,6,12M ,2,5,7,10,15,20,30Y time series whether treasuries or constant maturity yields. You will have position linked to each and you think or mentally monitor your pnl for each position. You have to reduce it to get a better idea of your PnL and in a scenario like that PCA is your best friend. It also helps with quick stress testing of extreme scenarios without re-pricing your whole portfolio.
Learning PCA and time series analysis can only help with jobs or keeping your job."